Progress of Non-Equilibrium Green's Functions 9 (PNGF9)

24 Aug 2026, 01:38 → 27 Aug 2026, 17:00 Europe/Zurich

Auditorium (Paul Scherrer Institut)

 

We are excited to announce the 9th installment of the Progress of Non-Equilibrium Green’s functions (PNGF9) conference! PNGF9 will take place at the Paul Scherrer Institute (PSI) in Switzerland.

 

PSI is Switzerland’s largest physics lab, and it can be reached from Zürich in about 40 minutes by public transportation. The conference aims to bring together researchers directly involved in development and application of non-equilibrium Green’s functions (NGF) methods, as well as young researchers, who address recent developments, current challenges and future perspectives. PNGF9 will bridge theory developments, algorithmic and computational advances, ab-initio approaches, and modeling experiments at large-scale research facilities.


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Monday 24 August

09:00 Registration

1 Tensor-Network Acceleration of diagrammatic calculations for quantum many-body systems out of equilibrium

Accurate diagrammatic simulations of nonequilibrium quantum many-body systems are often limited by the evaluation of multidimensional integrals involving high-order correlation functions. In this work, I present a tensor-network acceleration scheme for diagrammatic calculations based on tensor cross interpolation (TCI). The method is applied to the strong-coupling expansion for quantum impurity problems within dynamical mean-field theory (DMFT) and extended DMFT (EDMFT), enabling nonperturbative simulations of nonequilibrium steady states in both the Hubbard and extended Hubbard models. The central idea is to decompose multidimensional diagrammatic kernels on the fly into compact tensor-network representations, thereby substantially reducing the computational cost of evaluating contour-ordered correlators. Beyond impurity solvers, the same framework can be extended to higher-order spectroscopies such as time-resolved resonant inelastic X-ray scattering (tr-RIXS), which require the evaluation of four-point correlation functions.

Speaker: Martin Eckstein (University of Hamburg)

2 Quantics tensor trains and tensor cross interpolation for nonequilibrium Green's function simulations: algorithms and the tensor4all ecosystem

Nonequilibrium Green's function (NEGF) simulations face a steep growth of memory and computational cost with the number of time steps. Tensor networks offer a general solution: the quantics tensor train (QTT) representation compresses multi-time correlation functions by exploiting scale separation, and tensor cross interpolation (TCI) learns compressed tensor-train representations of functions and high-dimensional integrands from a small number of samples. In this talk, I give a pedagogical introduction to QTT and TCI: what they are, when and why they work, and how they can be used in practice through the open-source tensor4all ecosystem [1]. I briefly illustrate their potential with recent applications, including memory-efficient Kadanoff-Baym and GW simulations [2,3], a causality-based divide-and-conquer Dyson solver [4], weak-coupling TCI impurity solvers for equilibrium and nonequilibrium dynamical mean-field theory [5,6], and nonequilibrium two-particle correlation functions within a generalized Keldysh formalism [7]. Finally, I present tensor4all-rs, a new Rust-based library that unifies these tools, developed with systematic use of agentic coding and designed for HPC applications.

[1] Y. Núñez Fernández et al., SciPost Phys. 18, 104 (2025).
[2] M. Murray, H. Shinaoka, and P. Werner, Phys. Rev. B 109, 165135 (2024).
[3] M. Środa, K. Inayoshi, H. Shinaoka, and P. Werner, Phys. Rev. Lett. (2025), arXiv:2412.14032.
[4] K. Inayoshi, M. Środa, A. Kauch, P. Werner, and H. Shinaoka, SciPost Phys. 20, 077 (2026).
[5] S. Matsuura, H. Shinaoka, P. Werner, and N. Tsuji, Phys. Rev. B 111, 155150 (2025).
[6] S. Matsuura, H. Shinaoka, P. Werner, and N. Tsuji, arXiv:2607.00702.
[7] K. Inayoshi, H. Shinaoka, and Y. Murakami, arXiv:2607.11055.

Speaker: Hiroshi Shinaoka (Saitama University)

10:30 Coffee Break

3 Achieving optimal time scaling of Kadanoff-Baym equations for open systems

The exact dynamics of many-particle quantum systems coupled to an environment is governed by the Kadanoff-Baym equations. While these equations can, in principle, be solved exactly for small systems, the numerical cost grows rapidly and becomes prohibitive for longer times or larger systems. Beyond many-body correlations, the primary computational challenge arises from memory effects, which cause the numerical complexity to scale cubically with physical time. In certain cases, this scaling can be reduced to linear by reconstructing the lesser and greater Green’s function components from the electron density, however, at the expense of losing spectral information. It is demonstrated here that the Kadanoff-Baym equations for open systems can be solved numerically exactly with optimal quadratic time scaling, without introducing any approximations [Phys. Rev. B 113, L161111 (2026)].

As the first illustration, I will consider a correlated single-level quantum dot (QD) in the Coulomb blockade regime treated within the adiabatic TDDFT with the BALDA XC potential, and present two-time Green's functions and transient spectral functions for different bias voltages and temperatures. Then I will demonstrate that KBE are also compatible with nonadiabatic TDDFT treatment of the QD. Finally, I will discuss possible extensions of the idea towards correlated systems.

Speaker: Yaroslav Pavlyukh (Independent researcher)

4 Kadanoff-Baym approach to the bound-state problem in open quantum systems

In recent years the problem of bound-state formation in hot and dense medium in has become of high
interest in heavy-ion-collision theory due to the discovery at the LHC that the production rate of
light nuclei in ultra-relativistic heavy-ion collisions follows the statistical hadronization model with
abundancies consistent with the conditions at chemical freeze-out. Despite the small binding energies,
e.g., deuterons seem to be formed at a temperature of about 155 MeV.
In this work the problem is addressed within a non-relativistic quantum mechanical toy model applying
the Kadanoff-Baym many-body real-time contour approach to a particle moving in a potential, leading
to one or a few bound states in the vacuum, within a thermal bath. It is demonstrated that such a
model, following the properties of such Φ-derivable approximations, leads via rapid decoherence to the
proper equilibration of the particle with the heat bath and provides the full spectral information of the
one-particle state.

Speaker: Prof. Hendrik van Hees (Goethe University Frankfurt)

5 δNEGF: Quantum Fluctuations for Large-Scale Correlated Real-Time Dynamics

Computational many-body physics is governed by a persistent model–method dilemma. The finite resources available to a simulation must be divided between representing the physical system and solving its dynamics. A realistic Hamiltonian may require large basis sets, spatial inhomogeneity, and nonlocal interactions, whereas an accurate real-time propagation method must retain correlations, memory, and scattering while scaling favorably with system size and simulation time. Consequently, one typically chooses either sophisticated models combined with comparatively simple, often adiabatic dynamics, or advanced correlated solvers applied to reduced models. The regime in between—large, spatially complex, correlated systems driven far from equilibrium—has remained largely inaccessible.

Model downfolding, embedding, and low-rank compression techniques have steadily expanded the accessible range of many-body simulations, but mostly by shifting the compromise rather than removing it. To move beyond this limit, the two-particle correlations that carry memory and scattering must themselves be represented in a scalable form. δNEGF [1] provides such a representation: it reformulates nonequilibrium Green functions in terms of quantum fluctuations and replaces the explicit propagation of the rank-four two-particle correlation function by an ensemble of low-rank single-particle fluctuation trajectories. This retains dynamical self-energy effects and memory while substantially reducing runtime and memory requirements.

I will show how the resulting GW and particle-particle and particle-hole T-matrix schemes extend time-dependent dynamical NEGF simulations from approximately 10$^2$ to 10$^4$ basis states. Applications to diffusion in two-dimensional Hubbard systems and ultrafast dynamics in graphene-nanoribbon heterostructures illustrate regimes in which correlations and spatial complexity are simultaneously essential. The central implication is therefore not merely a computational speed-up: δNEGF changes the class of nonequilibrium many-body problems that can be addressed and can reveal phenomena previously hidden by computational limitations.

The talk will introduce δNEGF as a new route to scalable correlated real-time dynamics, emphasizing the computational idea behind the method, the physical regimes it opens, and future connections to embedding and first-principles modeling.

[1] E. Schroedter, M. Bonitz, and J.-P. Joost, arXiv:2606.10773

Speaker: Jan-Philip Joost (University of Kiel)

6 Nonequilibrium Green Functions for Large Correlated Systems

Correlated real-time dynamics in large, spatially inhomogeneous quantum systems remain a major challenge for nonequilibrium many-body approaches. Nonequilibrium Green functions (NEGF) provide a systematic and highly accurate framework for addressing this problem, but their practical application has long been limited by the cubic scaling of the computational runtime with the number of time steps, $N_t$. This bottleneck was recently overcome by the G1–G2 scheme [1], which achieves linear scaling in $N_t$. However, numerical instabilities become increasingly more prevalent at stronger coupling, and the explicit propagation of the two-particle Green function incurs a substantial memory overhead. Consequently, time-dependent simulations have so far remained limited to comparatively small systems with basis sizes of order $N_b\sim10^2$.

Here, we introduce a quantum-fluctuation formulation of nonequilibrium Green functions, denoted $\delta$NEGF [2], which addresses these limitations by representing two-particle correlations through fluctuations of field-operator products. The resulting formulation preserves the positivity of reduced density matrices, thereby stabilizing correlated dynamics, eliminates the explicit storage of the two-particle Green function, and maps the dynamics onto a finite ensemble of Hartree–Fock-like trajectories. Combined with a stochastic low-rank decomposition of the correlation functions, $\delta$NEGF substantially reduces the computational and memory requirements of advanced self-energy approximations, including GW and particle-particle as well as particle-hole T-matrix approximations, while retaining linear scaling in $N_t$.

We benchmark $\delta$NEGF against exact and HF-GKBA results for lattice systems and demonstrate its scalability in simulations reaching basis sizes of order $N_b\sim10^4$.

[1] Schlünzen et al., Phys. Rev. Lett. 124, 076601 (2020)

[2] Schroedter et al., arXiv:2606.10773 (2026)

Speaker: Erik Schroedter (Kiel University)

13:05 Lunch

7 A MOMENTUM-RESOLVED VIEW OF QUANTUM MATERIALS UNDER OPTICAL CONTROL

Time- and angle-resolved photoemission spectroscopy (ARPES) is an ideal experimental technique to access the transient electronic structure of quantum materials. Moreover, the simulation of ARPES spectra can be well achieved by calculating the spectral function through Green’s function-based methods.
Here I will exemplify how quantum material can be probed with time-resolved ARPES using two recent results from our laboratory at the University of Fribourg, with a focus on optical control. First, I will show how a tailored optical pulse can be used to generate a band inversion in a semiconductor to create a transient topological cone through Floquet engineering. Second, I will discuss how a resonant generation of excitons in a small gap semiconductor allows us to follow their decoherence into dark excitons.

Speaker: Prof. Claude Monney (University of Fribourg)

8 Hierarchical quasiparticle dynamics in antiferromagnets revealed by time- and momentum-resolved X-ray scattering

Low-energy collective excitations, such as phonons and magnons, are essential for understanding physics across a wide range of time and length scales. Energy flow among correlated subsystems, mediated by these collective excitations, is essential for ultrafast dynamics and high-speed technologies. Yet momentum-resolved access to low-energy magnons in non-equilibrium states has been lacking. In this talk, I will present a new technique, time-resolved resonant diffuse scattering, developed to close this gap. By combining complementary time-resolved X-ray techniques that elucidate the dynamics of the long-range antiferromagnetic state and low-energy phonons, as well as quantum-kinetic simulations, we unveil hierarchical energy pathways in the photoexcited antiferromagnet CuO [1]. The established microscopic framework, beyond phenomenological models, that should be applicable to other correlated materials.

References
[1] A. Romaguera, H. Ueda et al., arXiv: 2602.13113.

Speaker: Dr Hiroki Ueda (PSI - Paul Scherrer Institut)

9 Microscopic Origin of Local Spin Excitations in CrPS$_4$​ and PrAlGe probed by Core-Level X-ray Spectroscopy

Understanding how magnetic phase transitions in correlated quantum systems respond to external perturbations requires a rigorous many-body description of localized states and ligand coordination. Because these macroscopic states emerge from a subtle interplay between crystal-field effects, spin-orbit coupling, and strong electronic correlations, core-level techniques like X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS) take relevance. As element-specific probes, XAS and RIXS directly measure local cluster physics, core-hole multiplets, and crystal-field excitations. This provides a microscopic view of magnetism that complements macroscopic transport measurements; while transport probes the anomalous Hall effect (AHE) from delocalized conduction states, XAS and RIXS target localized orbitals to extract direct information about local magnetic moments.
To capture these dynamics, we developed a theoretical framework that maps first-principles Density Functional Theory (DFT) calculations to construct an Anderson Impurity Model (AIM) for localized subspaces, focusing on the 3$d$ shell for transition metals and the 4$f$ shell for rare earths. We use Dynamic Mode Decomposition (DMD) to discretize the hybridization, allowing us to mimic the host density of states (DOS) with a minimal number of bath sites. By solving the resulting finite-size Hamiltonian through exact diagonalization, we can compute core-level XAS/XMCD and RIXS/RIXS-MCD spectra to serve as direct fingerprints of the local magnetic states.
We applied this framework to resolve different physical phenomena in two different materials. For the magnetic system CrPS$_4$, we analyze spin-flip excitations using a minimal model that couples local spin flips to the crystal-field manifold, capturing how these excitations track the broader magnetic phase transitions. For the magnetic Weyl candidate PrAlGe, we model the Pr 4$f$-4$f$ excitations to explain why local magnetic moments and circular dichroism persist up to $T \sim 35$ K, well above the bulk ferromagnetic transition at $T_c \sim 16$ K.

Speaker: Juan Felipe Pulgarin Mosquera (University of Fribourg)

16:15 Welcome Apéro

Tuesday 25 August

10 Nonequilibrium Green’s function theory for dissipative (non-unitary) dynamics

Dissipation is usually associated with decoherence and loss of quantum properties. However, in interacting many-body systems it can also stabilize unconventional states, and profoundly modify electronic, optical and topological properties. Describing these phenomena requires a framework capable of treating interactions, external driving, and environmental effects on the same footing.
In this talk, I will present the nonequilibrium Green’s-function theory of interacting systems governed by the dissipative (non-unitary) Lindbladian dynamics. By reformulating the Keldysh construction in second quantization, we extend diagrammatic perturbation theory to many-body dissipative processes, and present the corresponding Kadanoff–Baym equations.
The resulting framework preserves much of the structure and versatility of conventional nonequilibrium Green’s-function methods for isolated systems. It therefore provides a foundation for correlated simulations of transient and steady-state phenomena in dissipative materials.

Speaker: Gianluca Stefanucci (University of Rome Tor Vergata)

11 Efficient Nonequilibrium Green’s Function Methods for Time-Resolved Spectroscopy

Time-resolved spectroscopies provide direct access to observables that encode information about transient excited states and dynamical correlations in quantum materials. In this talk, I will present recent developments in efficient diagrammatic approaches for computing time-resolved spectral functions, centered on the Real-Time Dyson Expansion (RTDE), which reconstructs the time-nonlocal correlations through a perturbative expansion around nonequilibrium reduced density matrix trajectories while retaining the favorable scaling of single-time propagation schemes. I will discuss recent extensions of this framework to driven-dissipative systems, comparisons with the Kadanoff-Baym equations and the generalized Kadanoff-Baym ansatz. Further, I will comment on the role of self-consistency and Markovianity in describing transient spectral properties. Applications to photoexcited correlated semiconductors demonstrate the emergence of excitonic satellites, quasiparticle renormalization, and band-gap dynamics, illustrating how efficient NEGF methods can provide predictive simulations of modern ultrafast spectroscopic experiments.

Speaker: Prof. Vojtěch Vlček (UC Santa Barbara)

12 MBPT for driven dissipative open quantum systems

We present a unified many-body perturbation theory for open quantum systems, that treats dissipation, correlations, and external driving on equal footing. Using a Keldysh–Lindblad formalism, we introduce diagrammatic treatment of dissipative interaction lines representing quasiparticle flows and fluctuations. Two new Feynman rules render the evaluation of dissipative diagrams compact and systematically improvable, while preserving the Keldysh and anti-Hermitian symmetries of the closed-system theory. Consequently, the structure of the Kadanoff–Baym equations (KBE) remains unchanged, enabling existing numerical methods to be directly applied. To illustrate this, we derive dissipative versions of the second Born and GW approximations, identifying the physical content of the self-energy components. Moreover, we demonstrate that time-linear approximations to the full KBE retain their closed structure and can be efficiently used to simulate relaxation and decoherence dynamics. This framework establishes a general route toward first-principles modeling of correlated, driven, and dissipative quantum materials.

Speaker: Thomas Blommel (UCSB)

10:30 Coffee Break

13 Non-Hermitian Bethe-Salpeter Equation for Open Systems: Emergence of Exceptional Points in Excitonic Spectra from First Principles

In open quantum systems hosting excitons, dissipation mechanisms critically shape the excitonic dynamics, band-structure and topological properties. A microscopic understanding of excitons in such non-Hermitian settings demands a first-principles generalization of the Bethe-Salpeter equation (BSE). Building on a recently introduced nonequilibrium Green’s function formalism compatible with Lindbladian dynamics, we derive a non-Hermitian BSE from diagrammatic perturbation theory on the Keldysh contour, and obtain a microscopic excitonic Hamiltonian that incorporates dissipation while preserving causality. We apply the formalism to valley excitons in transition metal dichalcogenides coupled to structured photon baths. We uncover a rich landscape of exceptional points in momentum space, forming either discrete sets or continuous manifolds, depending on bath structure. The exceptional points give rise to non-analytic valley-polarization, unusual polarization pattern in photoluminescence, and nontrivial topological signatures. Our results establish a first-principles framework for predicting and controlling excitonic behavior in open quantum materials, showing how engineered environments can be leveraged to induce and manipulate non-Hermitian and topological properties.

Speaker: Zhenlin Zhang (University of Science and Technology of China)

NH-BSE-Slide.pdf

Non-Hermitian Bethe-Salpeter Equation for Open Systems: Emergence of Exceptional Points in Excitonic Spectra from First Principles

14 First-Principles Exciton–Phonon Dynamics

Exciton dynamics—including ultrafast photogeneration, diffusion, and thermalization—plays a central role in optoelectronic, photovoltaic, and photocatalytic processes. In this talk, I will present a novel first-principles many-body framework for describing exciton dynamics driven by electron–phonon interactions. A key ingredient of the theory is the introduction of an auxiliary excitonic species, referred to as the irreducible exciton, which eliminates the overscreening of the electron–phonon interaction that arises in conventional approaches. The resulting Excitonic Bloch Equations retain a computational cost comparable to that of the widely used Excitonic Boltzmann Equations while providing a unified description of the time evolution of coherent, irreducible, and incoherent excitons during and after optical excitation. As an application, I will discuss the real-time formation of excitons in monolayer WSe2, revealing how above-bandgap photoexcitation initially generates quasi-free electron–hole pairs that are subsequently converted into bound excitons through their interaction with phonons.

Speaker: Enrico Perfetto (University of Rome Tor Vergata)

15 Efficient nonequilibrium electron dynamics from first-principles: leveraging Koopmans spectral functionals and Wannier localization

We present an efficient first-principles approach to nonequilibrium electron dynamics in extended systems, leveraging Koopmans-compliant spectral functionals and Wannier functions. Koopmans functionals provide an accurate description of the quasiparticle band structure, which serves as the static starting point for real-time propagation of the electronic density matrix within the Hartree-plus-screened-exchange (HSEX) approximation. The use of localized Wannier functions significantly reduces the computational cost and memory footprint, enabling simulations of larger systems and longer timescales. The HSEX self-energy is efficiently evaluated using density-functional perturbation theory, avoiding explicit calculation of unoccupied states and dielectric matrices. Benchmark calculations reproduce experimental and GW-BSE optical absorption spectra across systems with weakly and strongly bound excitons. We then apply the framework to high-harmonic generation (HHG) showing that the harmonic emission is selectively enhanced at excitonic resonances, providing direct evidence that HHG probes correlated electron-hole excitations rather than the quasiparticle band structure alone.

Speaker: Nicola Colonna (PSI - Paul Scherrer Institut)

16 Towards capturing dynamical screening with a Sternheimer Bethe-Salpeter ansatz

An accurate description of adsorption on metal surfaces requires to take into account the image charge which is generated within the metal surface [1]. State-of-the-art semilocal and hybrid exchange-correlation functionals are incapable to capture the substrate polarization, thus emphasizing the necessity of dynamical screening as incorporated in GW and Bethe-Salpeter ansätze. Based on our recent work on time-dependent density functional theory ansätze within the Sternheimer formulation [2,3], Sternheimer Bethe-Salpeter ansätze will be presented implying exact or semi-empirical electron repulsion operators. Relying on the mixed Gaussian and plane wave framework of the quantum-mechanical program package CP2K [4] as well as on thereon based GW implementations [5,6] enables favorable scaling with system size, paving the way towards applications on solids, surfaces and condensed-phase systems.

[1] J. M. Garcia-Lastra, C. Rostgaard, A. Rubio, K. S. Thygesen, Phys. Rev. B 80, 245427 (2009).
[2] A. Hehn, B. Sertcan, F. Belleflamme, S. K. Chulkov, M. B. Watkins, J. Hutter, J. Chem. Theory Comput. 12, 4186 (2022).
[3] B. Sertcan Gökmen, J. Hutter, A. Hehn, J. Chem. Theory Comput. 20, 8494 (2024).
[4] M. Iannuzzi et. al., J. Phys. Chem. 130, 1237 (2026).
[5] J. Wilhelm, D. Golze, L. Talirz, J. Hutter, C. A. Pignedoli, J. Phys. Chem. Lett. 9, 306312 (2018).
[6] R. Pasquier, M. Camarasa-Gomez, A. Hehn, D. Hernangomez-Perez, J. Wilhelm, Phys. Rev. B 112, 205130 (2025).

Speaker: Anna Hehn (Christian-Albrechts-University Kiel)

17 Linear-Time Simulation of Two-Time Non-Markovian Dynamics with Systematically Controllable Accuracy

The time-resolved angle-resolved photoemission spectra of WSe$_2$, a paradigmatic transition metal dichalcogenide, are dominated by a transient signal that, after being initially observed in the gap at the $K$ valley, scatters, on an ultra-fast time scale of $\sim\,30$ fs, to the $\Sigma$ valley. In this work we question the common interpretation of the experimental dynamics in terms of a massive bound electron-hole exciton that scatters with phonons and behaves as a quasi-particle. By using a combined theoretical and experimental investigation, we demonstrate that the observed dynamics can be interpreted as the photo-induced transition from direct to indirect excitonic-insulating order. The features that appear in the experimental spectrum correspond to single-particle levels renormalized by the excitonic spontaneous polarization.

Speaker: Kai Wu (Institute of Structure of Matter, National Research Council of Italy)

13:00 Lunch

18 Non-equilibrium Exciton Dynamics in Solids: A First-Principles Perspective

Understanding nonequilibrium quasiparticle dynamics in materials requires going beyond static electronic structure. Here, we present an ab initio framework that combines GW/BSE with real-time quantum dynamics to simulate exciton dynamics in different materials. It is shown that exciton dynamics is fundamentally driven by different many-body interactions. In transition metal dichalcogenides, exchange interaction enables ultrafast valley depolarization by opening intervalley channels forbidden in a single-particle picture. Furthermore, phonons act as a dynamical switch that activates long-range Coulomb coupling, leading to rapid bright-to-dark exciton relaxation. When electron-phonon coupling are strong enough, it can also dress the exciton and form polaron-exciton in polar materials. We reveal the formation of dynamically fluctuating polaron–exciton states in TiO₂, where electron–phonon coupling and Coulomb interaction cooperatively determine the quasiparticle properties and lifetimes.

Speaker: Jin Zhao (University of Science & Technology of China)

19 Electron-phonon interactions in the time domain: from non-equilibrium phonon dynamics to theoretical spectroscopy

First-principles simulations of electron–phonon interactions (EPI) are key to clarifying the microscopic origin of the ultrafast electron and phonon dynamics revealed by pump–probe experiments. In this talk, I will discuss recent advances in ab-initio simulations of the EPI and their application to light-driven electron and lattice dynamics. Building on recent progress in many-body theory and software, predictive atomistic simulations of complex non-equilibrium phenomena have now become feasible. I will highlight, in particular, non-thermal phonon populations [1], coherent phonons [2], and ultrafast polaron formation as representative examples [3]. This progress forms the basis for a strong synergy between ab-initio theory and experimental ultrafast science.

[1] Pan et al., ACS Nano 19, 11381 (2025).
[2] Emeis et al., Phys. Rev. X 15, 021039 (2025).
[3] Garcia-Herrero et al., arXiv 2601.21810 (2026)

Speaker: Fabio Caruso

15:45 Coffee Break / Discussions

Wednesday 26 August

20 Compact Representations of Response Functions

Response functions are fundamental objects in quantum many-body theory. For equilibrium and steady-state systems, retarded response functions are analytic in the upper half of the complex plane, and their imaginary part has a definite sign. These analytic properties enable compact and systematically improvable representations based on pole approximants and moment theory, allowing high-precision calculations while significantly reducing computational complexity. This talk will provide an overview of the underlying analytic structure, introduce controlled approximation schemes, and discuss their application to the efficient computation of response functions.

Speaker: Emanuel Gull (University of Warsaw & University of Michigan)

21 Generalized Keldysh formalism for nonequilibrium correlation functions and its quantics-tensor-train implementation

Recent developments in time-resolved Raman scattering [1] and resonant inelastic X-ray scattering [2,3] have enabled the observation of the time evolution of various low-energy excitations, such as charge, spin, and phonon excitations, in materials. From a theoretical perspective, the spectra of these excitations can be computed from the nonequilibrium two-particle correlation functions. To compute the time evolution of these correlation functions, one can straightforwardly solve the nonequilibrium Bethe–Salpeter equation, but this incurs prohibitive computational and memory costs. Therefore, conventional approaches often neglect vertex corrections (the bubble approximation) [4], which is inconsistent with the Baym–Kadanoff conserving approximation.

To overcome this difficulty, we propose an approach to calculate nonequilibrium correlation functions, naturally including vertex corrections, using the generalized Keldysh formalism [5] for a Hamiltonian that includes a virtual external probe field [6]. In particular, we introduce a Bethe–Salpeter-like integral equation for correlation functions and develop an efficient solver of this equation with quantics tensor trains (QTT) [7–11].

In this talk, we present this formalism together with its QTT implementation, and apply it to the fluctuation dynamics of nonequilibrium antiferromagnetic states in the Hubbard model. We find that the dynamics differs qualitatively depending on whether vertex corrections are included, and that, as the system approaches a nonthermal critical point, the maximum value and the decay time of the fluctuations increase [12].

[1] J.-A. Yang et al., Sci. Rep. 7, 40876 (2017).
[2] M. Dean et al., Nature Mat. 15, 601 (2016).
[3] M. Mitrano and Y. Wang, Commun. Phys. 3, 184 (2020).
[4] P. Werner, M. Eckstein and N. Tsuji, Phys. Rev. B 108, 245157 (2023).
[5] E. Canovi, P. Werner and M. Eckstein, Phys. Rev. Lett. 113, 265702 (2014).
[6] O. P. Matveev, A. M. Shvaika, and J. K. Freericks, Phys. Rev. B 113, 195148 (2026).
[7] H. Shinaoka et al., Phys. Rev. X 13, 021015 (2023).
[8] M. Murray, H. Shinaoka, and P. Werner, Phys. Rev. B 109, 165135 (2024).
[9] M. Środa, K. Inayoshi, H. Shinaoka, and P. Werner, Phys. Rev. Lett. 135, 226501 (2025).
[10] K. Inayoshi, M. Środa, A. Kauch, P. Werner, and H. Shinaoka, SciPost Phys. 20, 077 (2026).
[11] M. Środa, K. Inayoshi, M. Schüler, H. Shinaoka, and P. Werner, Phys. Rev. B 113, 165113 (2026).
[12] K. Inayoshi, H. Shinaoka, and Y. Murakami, arXiv:2607.11055.

Speaker: Dr Ken Inayoshi (Department of Physics, Saitama University)

22 Tensor-train impurity solver for nonequilibrium DMFT and Thermalization dynamics in the Hubbard model

Nonequilibrium dynamical mean-field theory (DMFT) is a powerful framework for studying the real-time dynamics of strongly correlated electron systems. In this approach, an interacting lattice model such as the Hubbard model is mapped onto a quantum impurity problem, but solving this impurity problem accurately remains the central numerical bottleneck. Continuous-time quantum Monte Carlo (CT-QMC) impurity solvers systematically sum high-order Feynman diagrams and have been highly successful in equilibrium. In nonequilibrium problems, however, they suffer from the dynamical sign problem, which has severely restricted numerically accurate simulations to limited settings.
To overcome this limitation, we implement a deterministic impurity solver based on the weak-coupling expansion and the tensor-train decomposition with tensor cross interpolation (TCI) [1,2]. The method approximates the high-dimensional integrands of Feynman diagrams in a tensor-train format and evaluates the integrals without stochastic sampling [3]. This makes the method suitable for regimes where Monte Carlo sampling is strongly affected by sign or phase cancellations.
In this talk, I will explain the formulation of our tensor-train impurity solver and discuss its application to nonequilibrium DMFT calculations for interaction quenches in the Hubbard model. I will particularly focus on thermalization dynamics away from half filling, where particle-hole symmetry is broken and previous CT-QMC-based studies have been strongly hindered by the sign problem. Using the tensor-train-based nonequilibrium DMFT approach, we investigate how the fast thermalization and dynamical transition known at half filling [4] are affected by doping.

References:
[1] S. Matsuura, H. Shinaoka, P. Werner, and N. Tsuji, Phys. Rev. B 111, 155150 (2025).
[2] S. Matsuura, H. Shinaoka, P. Werner, and N. Tsuji, arXiv:2607.00702 (2026).
[3] Y. Núñez Fernández et al., Phys. Rev. X 12, 041018 (2022).
[4] M. Eckstein, M. Kollar, and P. Werner, Phys. Rev. Lett. 103, 056403 (2009).

Speaker: Mr Shuta Matsuura (The University of Tokyo)

23 Bold hybridization expansions for impurity models

In recent years, several non-stochastic algorithms have been developed for solving impurity models using the hybridization expansion, such as tensor cross interpolation, quasi–Monte Carlo integration, and sum-of-exponentials-based separation of variables.

While it is extremely hard to outperform Philipp Werner's (stochastic) continuous-time quantum Monte Carlo hybridization expansion in equilibrium, the non-stochastic direct-integration approaches have the benefit of also being applicable in real time and out of equilibrium.

I will present open-source implementations of quasi–Monte Carlo integration for the inchworm expansion and of sum-of-exponentials separation of variables applied to the bold self-energy approach, currently limited to the imaginary-time contour branch, and give an outlook on extending both approaches to the real-time non-equilibrium case.

Speaker: Hugo U. R. Strand (Örebro University)

10:35 Coffee Break

24 transverse cRPA and the Hubbard model in a polaritonic near-field

The influence of the dielectric environment on material properties has been studied theoretically mostly within two different contexts: Within Coulomb engineering one uses electrostatic screening of the longitudinal electromagnetic field to renormalize interactions. In contrast, within cavity material engineering one tries to shape the modes of the enveloping electromagnetic field to produce desired material properties. For these settings we present a unifying gauge consistent description in the form of the constraint random phase approximation extended to the transverse components of the electromagnetic field. Using this formalism we derive the action and Hamiltonian for the Hubbard model in the near-field of surface phonon-polaritons. We compute its phase diagram using DMFT + GW, where we find a shift of the metal-to-insulator transition near the surface. We compare this shift in different gauges.

Speaker: Paul Fadler (University of Bremen)

25 Superconductivity in photo-doped Mott insulators

We use nonequilibrium dynamical mean field theory (DMFT) in combination with strong-coupling impurity solvers to study eta-pairing states in photo-doped Mott insulators. To achieve reasonably accurate DMFT solutions, the strong coupling technique is combined with quantics tensor cross interpolation for the efficient evaluation of the diagram weights.

Speaker: Philipp Werner (University of Fribourg)

26 Hierarchical approach to compressed Greens functions

We present recent developments in hierarchical representations of nonequilibrium Green’s functions, including applications and open challenges. We begin by comparing global iterative solvers, which suffer from error-front propagation, with time-stepping approaches that avoid this limitation. We show that hierarchical representations have become a practical tool for contemporary problems, including applications to driven superconducting and excitonic systems. Through the development of the open-source H-NESSi library, these methods are made accessible to the broader community. As a main application, we present transport calculations for the weakly interacting two-dimensional Hubbard model, where hierarchical time representations enable simulations of large lattices and calculations of the optical response and DC conductivity at very low temperatures. Preliminary results reveal a broad regime of linear resistivity at weak coupling, characteristic of strange-metal behaviour. We conclude with a discussion of the remaining challenges in extending these methods to realistic systems.

Speaker: Dr Denis Golez (Jožef Stefan Institute)

13:00 Lunch

15:00 Social Event

Thursday 27 August

27 Time-linear scaling nonequilibrium transport and thermoelectricity beyond the wide-band limit

Accurate modeling of nanoscale transport requires a simultaneous treatment of quantum coherence, interactions, and nonequilibrium environments. While the wide-band limit often enables substantial simplifications, it neglects reservoir spectral structure and can limit the quantitative description of transport and thermodynamic processes. We present a nonequilibrium Green's function framework for open quantum systems beyond the wide-band approximation. Using a finite-bandwidth representation of the reservoirs, the resulting equations of motion retain time-linear scaling while providing direct access to time-dependent charge, energy, and heat currents [1]. The approach enables efficient simulations of interacting quantum junctions coupled to structured environments. Beyond transport calculations, the formalism establishes a connection between nonequilibrium current responses and spectral properties of the central system. In multiterminal geometries, current-voltage characteristics can be used to reconstruct features of the underlying many-body spectrum, providing a transport-based spectroscopic tool [2]. Applications to molecular thermoelectric devices demonstrate how reservoir spectral structure, interactions, and nonequilibrium driving jointly influence energy-conversion efficiency. The framework thus provides a versatile platform for studying and optimizing thermoelectric performance in nanoscale systems operating far from equilibrium [3].

[1] Y. Pavlyukh and R. Tuovinen, Phys. Rev. B 111, L241101 (2025).
[2] Y. Pavlyukh and R. Tuovinen, Eur. Phys. J. Spec. Top. (2025).
[3] R. Tuovinen and Y. Pavlyukh, PRX Energy 4, 043003 (2025).

Speaker: Riku Tuovinen (University of Jyväskylä)

28 Nonperturbative Nonlinear Hall Effect in Nonequilibrium Steady States

The nonlinear Hall effect in quantum materials has attracted broad interest; yet most existing studies focus on the weak-field, perturbative regime.
Here we develop a nonperturbative approach based on nonequilibrium steady-state Green's functions for dc-field-driven lattice systems, with dissipation and interactions incorporated through self-energies beyond the constant relaxation-time approximation and interband transitions treated alongside their intraband counterparts.
Applied to a two-band semimetal model, our approach provides direct access to the strong-field Hall response beyond the nonperturbative crossover where the edge of the nonequilibrium distribution reaches Berry-curvature hot spots, a regime in which constant relaxation-time estimates and Berry curvature dipole calculations become unreliable.
We further demonstrate that interaction and electron-phonon self-energies within dynamical mean-field theory can substantially enhance the Hall signal.
Our framework enables quantitative simulations of nonequilibrium nonlinear Hall phenomena and provides guidance for strong-field transport experiments.

Speaker: Lei Geng (University of Fribourg)

29 Nanoscale Device Modelling beyond the Ballistic Limit of Transport

Computer-aided design tools dedicated to the modelling of nano-devices, e.g., transistors, memory cells, or photo-detectors, should capture quantum mechanical effects from first-principles and account for non-ideal phenomena such as electron-phonon or electron-electron interactions. In this presentation, a framework called QuaTrEx that fulfils these criteria will be presented, focusing on its simulation capabilities, algorithms, and implementation strategy. Concrete examples demonstrating the benefit of the chosen approach will be discussed.

Speaker: Mathieu Luisier (ETH Zurich)

10:30 Coffee Break

30 Gauge invariant derivation of the matter–only Hamiltonian

Enrico Fermi in 1932, used classical Gauss equation to derive the Coloumb density–density interaction from the longitudinal electro–magnetic potential, in a gauge–invariant way. In this work we extend the Fermi procedure to the transverse component of the vector potential. By using a fully quantistic canonical transformation we replace the transverse vector potential with a current– current and current–current–density interactions. The transformed Hamiltonian is, then, projected in the fermionic space providing a matter–only gauge respecting Hamiltonian. We discuss how this Hamiltonian provides the quantistic origin of the longitudinal–transverse splitting observed in phonons and other elemental excitations.

Speaker: Andrea Marini (CNR-ISM)

31 Floquet Engineering of Quantum Materials Beyond Idealized Conditions: A Nonequilibrium Green's Function Perspective

Periodic driving of solids offers new opportunities for controlling and designing quantum phases of matter. Floquet engineering has, for example, been proposed as a route to induce topological states in graphene through circularly polarized light [1, 2] . However, the persistence of Floquet states under realistic conditions, including interactions, screening, and decoherence, remains an open question.
In this contribution, we explore extensions of the Floquet nonequilibrium Green's function formalism [3] aimed at describing driven materials beyond idealized settings. These developments enable the inclusion of electronic interactions, phonon scattering, and electromagnetic screening effects within a unified framework. The treatment of Coulomb interactions and electron--phonon coupling may, for instance, be formulated using self-energy approximations such as the second Born and Migdal approaches [4], while self-consistent coupling to Maxwell equations provides access to screening and feedback effects in driven systems [5].
Such extensions provide a foundation for assessing the realistic prospects of Floquet engineering in solids and for identifying regimes in which nonequilibrium phases may be stabilized. As a longer-term perspective, we discuss how this framework could be employed to investigate dynamical instabilities in periodically driven quantum materials [6].
[1] Oka et al. PRB 79, 081406(R) (2009)
[2] McIver et al. Nat. Phys. 16, 38–41 (2020)
[3] Tsuji et al., PRB 78 235124 (2008)
[4] Schüler et al. PRX 10 041013 (2020)
[5] Ong et al. arXiv:2504.00583 (2025)
[6] Okuwaga et al. arXiv:2601.04451 (206)

Speaker: Nils Jacobsen (Universität Bremen, MPSD Hamburg)

32 Efficient scanning-probe spectroscopy using Wannier-based nonequilibrium Green's functions

Scanning tunneling microscopy and spectroscopy (STM/STS) provide powerful tools for probing electronic properties at the atomic scale. On the theoretical side, density functional theory (DFT) and Wannier-based methods allow realistic first-principles descriptions of complex nanosystems. However, modeling nonequilibrium transport remains a significant challenge, especially in superconducting hybrid systems where particle-hole correlations must be treated explicitly. Accurate and efficient theoretical simulations are therefore essential for interpreting experimental measurements and understanding the underlying transport mechanisms.
Here, we present a workflow that combines Wannierized first-principles electronic structure calculations with the nonequilibrium Green's function formalism to enable efficient simulations of STM experiments [1]. This approach builds upon standard DFT packages to construct compact transport Hamiltonians that retain the electronic properties of realistic materials. Superconductivity is incorporated through an effective pairing potential within the Nambu-spinor formalism, while the coupling to the STM tip and substrate electrodes is treated within the wide-band limit approximation.
Within this framework, transport quantities such as current-voltage characteristics are evaluated in closed analytical form. This substantially reduces the computational cost of spectroscopic calculations. The method provides a unified and computationally efficient approach for modeling superconducting hybrid nanostructures featuring spin-orbit coupling, magnetic textures, and spin polarization. Representative applications demonstrate its robustness and versatility for both simple model systems and realistic ab initio molecular structures relevant to modern STM experiments.

[1] O. Moreno Segura et al., manuscript in preparation (2026).

Speaker: Oscar Moreno Segura (University of Jyväskylä)

33 Tackling the multi-reference problem for molecules with the TD2RDM method

Capturing correlation effects in quantum many-body systems remains a major challenge in the physical description of molecules. Coupled cluster theory has proven to be very accurate in a weakly interacting, weakly correlated setting while scaling comparatively favourably with system size. However, it struggles with systems with large static correlations. This issue is known as the multi-reference problem as conventional coupled cluster approaches rely on a single Slater determinant as their reference state and struggle with systems that cannot adequately be approximated this way. Examples for such systems are molecules whose geometries differ from the equilibrium configuration, for instance molecules adsorbed to surfaces. The time-dependent two-particle reduced density matrix (TD2RDM) method has the same system size scaling as time-dependent extensions of coupled cluster singles doubles theory without relying on the choice of a reference state. Thus, it is a promising alternative for the description of molecules and other correlated systems with multi-reference character.
In this work, we present first results for the application of the TD2RDM method to small molecular systems. We compare results with coupled cluster theory, time-dependent Hartree Fock, as well as numerically exact calculations. In particular, we address the issue of robustness of these approaches with respect to the multi-reference character of the simulated system. To this end, we analyse the simulation results of these methods for molecular systems with increasingly stretched bonds.

Speaker: Marie Eder

12:35 Closing remarks

13:00 Lunch