Entanglement Scaling and Criticality with Tensor Networks

28 Nov 2022, 09:00 → 2 Dec 2022, 16:00 Europe/Zurich

Bernoulli Center, EPFL

Andreas Läuchli (PSI - Paul Scherrer Institut & EPFL, Switzerland), Frank Verstraete (Ghent University, Belgium), Laurens Vanderstraeten (Ghent University, Belgium)

The description of critical phenomena in terms of the renormalization group forms the cornerstone of our modern understanding of strongly-correlated systems. It leads to effective Hamiltonians that can be studied using numerical methods such as Monte Carlo, and the success of those methods relies heavily on scaling ideas for the interpretation of the data. Based on the density matrix renormalization group and insights from the theory of entanglement in quantum information, tensor networks have recently emerged as a viable and wider applicable alternative for the numerical study of strongly-correlated systems. In essence, tensor networks describe many-body wavefunctions in terms of local tensors expressing how entanglement is routed. Although critical phenomena have been studied successfully using tensor networks and finite-entanglement scaling ideas have been formulated, the full problem of scaling has never been addressed in its full power and generality.

The main goal of this workshop is to bring world experts in critical phenomena and tensor networks together to put the framework of entanglement scaling on a firm theoretical footing. We have identified three different communities that are relevant to this endeavour: 1. the community working on conformal field theory and boundary conformal field theory, including finite-size scaling methods; 2. experts in the field of tensor networks; 3. people working in the field of quantum simulation of quantum field theories, in which similar problems arise.

Supported by the Bernoulli Center at EPFL.

Organizers

Andreas Läuchli (PSI/EPFL)
Laurens Vanderstraeten (UGent)
Frank Verstraete (UGent)

Confirmed Invited Participants

M.C. Banuls (Garching)
J. Bridgeman (Ghent)
P. Calabrese (Trieste)
N. Chepiga (Delft)
P. Corboz (Amsterdam)
P. Fendley (Oxford)
V. Gorbenko (Lausanne)
J. Hasik (Amsterdam)
F. Mila (Lausanne)
V. Pasquier (Saclay)
D. Poilblanc (Toulouse)
F. Pollmann (Garching)
S. Rychkov (Paris)
H. Saleur (Paris/Los Angeles)
N. Schuch (Vienna)
M. Schuler (Innsbruck)
L. Tagliacozzo (Madrid)
A. Tilloy (Paris)
E. Tonni (Trieste)
U.-J. Wiese (Bern)

Monday 28 November

10:00 → 11:00 Symmetric PEPS analysis of a phase transition in coupled spin-1/2 ladders

Speaker: Juraj Hasik

Hasik.pdf

11:00 → 11:30 Coffee Break

11:30 → 12:30 Open issues on finite entanglement scaling, the case of the transfer matrix spectrum

Speaker: Luca Tagliacozzo

Tagliacozzo.pdf

12:30 → 14:30 Lunch Break

14:30 → 15:30 Defects, Duality and Categorical Symmetries

Speaker: Paul Fendley

Fendley.pdf

15:30 → 16:00 Coffee Break

16:00 → 17:00 Relativistic matrix product states and an application to the Sinh-Gordon model

Speaker: Antoine Tilloy

Tilloy.pdf

Tuesday 29 November

09:00 → 10:00 Light cone tensor network and time evolution

Speaker: Mari-Carmen Banuls

Banuls.pdf

10:00 → 11:00 Peculiarities of RG flows in 2d O(n) models

Speaker: Victor Gorbenko

Gorbenko.pdf

11:00 → 11:30 Coffee Break

11:30 → 12:30 Torus spectroscopy of quantum critical points: A fingerprint of higher-dimension conformal field theories

Speaker: Michael Schuler

Schuler.pdf

12:30 → 14:30 Lunch Break

14:30 → 15:30 Applications of finite correlation length scaling with iPEPS

Speaker: Philippe Corboz

Corboz.pdf

15:30 → 16:00 Coffee Break

16:00 → 17:00 Solution of theta-Vacuum and Chemical Potential Sign Problems in CP(N-1) Models Regularized with SU(N) Quantum Spin Ladders

Speaker: Uwe-Jens Wiese

Wiese.pdf

17:00 → 19:00 Poster Session

Wednesday 30 November

09:00 → 10:00 Deterministic dynamics of initially random systems

Speaker: Vincent Pasquier

Pasquier.pdf

10:00 → 11:00 Critical properties of the interacting Majorana chain. The power of Friedel oscillations

Speaker: Natalia Chepiga

Chepiga.pdf

11:00 → 11:30 Coffee Break

11:30 → 12:30 Does tensor RG converge because of truncation effects?

Speaker: Slava Rychkov

12:30 → 14:30 Lunch Break

14:30 → 15:30 Lower bounds on ground state energies from tensor networks

Speaker: Norbert Schuch

15:30 → 16:00 Coffee Break

16:00 → 17:00 Finite-Size “Level Spectroscopy” Approach with Tensor Network Renormalization

Speaker: Masaki Oshikawa

Oshikawa.pdf

19:30 → 21:30 Workshop Dinner Restaurant Le Debarcadere in St. Sulpice

Restaurant Le Debarcadere in St. Sulpice.
https://restaurant.ledebarcadere.ch/

Thursday 1 December

09:00 → 10:00 Entanglement, symmetries, and asymmetry

Speaker: Pasquale Calabrese

Calabrese.pdf

10:00 → 11:00 Investigating thermal critical points with tensor networks

Speaker: Frederic Mila

Mila.pdf

11:00 → 11:30 Coffee Break

11:30 → 12:30 Entanglement entropies for Lifshitz fermionic fields at finite density

Speaker: Erik Tonni

12:30 → 14:30 Lunch Break

14:30 → 15:30 Finite-depth scaling of infinite quantum circuits for quantum critical points

Speaker: Frank Pollmann

Pollmann.pdf

15:30 → 16:00 Coffee Break

16:00 → 17:00 Tensor network algorithms for high-dimensional quantum many-body systems

Speaker: Simone Montangero

17:00 → 18:00 Discussion Session

Friday 2 December

09:00 → 10:00 Tensor Networks Can Resolve Fermi Surfaces

Speaker: Quinten Mortier

Mortier.pdf

10:00 → 11:00 Tensor network approach for 2D chiral spin liquids

Speaker: Didier Poilblanc

11:00 → 11:30 Coffee Break

11:30 → 12:30 A scaling hypothesis for PEPS and MPS

Speaker: Bram Vanhecke

Vanhecke.pdf

12:30 → 13:30 Closing, Lunch and Departure