Entanglement Scaling and Criticality with Tensor Networks

Europe/Zurich
Bernoulli Center, EPFL

Bernoulli Center, EPFL

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

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)

    • 10:00 AM 11:00 AM
      Symmetric PEPS analysis of a phase transition in coupled spin-1/2 ladders 1h
      Speaker: Juraj Hasik
    • 11:00 AM 11:30 AM
      Coffee Break 30m
    • 11:30 AM 12:30 PM
      Open issues on finite entanglement scaling, the case of the transfer matrix spectrum 1h
      Speaker: Luca Tagliacozzo
    • 12:30 PM 2:30 PM
      Lunch Break 2h
    • 2:30 PM 3:30 PM
      Defects, Duality and Categorical Symmetries 1h
      Speaker: Paul Fendley
    • 3:30 PM 4:00 PM
      Coffee Break 30m
    • 4:00 PM 5:00 PM
      Relativistic matrix product states and an application to the Sinh-Gordon model 1h
      Speaker: Antoine Tilloy
    • 9:00 AM 10:00 AM
      Light cone tensor network and time evolution 1h
      Speaker: Mari-Carmen Banuls
    • 10:00 AM 11:00 AM
      Peculiarities of RG flows in 2d O(n) models 1h
      Speaker: Victor Gorbenko
    • 11:00 AM 11:30 AM
      Coffee Break 30m
    • 11:30 AM 12:30 PM
      Torus spectroscopy of quantum critical points: A fingerprint of higher-dimension conformal field theories 1h
      Speaker: Michael Schuler
    • 12:30 PM 2:30 PM
      Lunch Break 2h
    • 2:30 PM 3:30 PM
      Applications of finite correlation length scaling with iPEPS 1h
      Speaker: Philippe Corboz
    • 3:30 PM 4:00 PM
      Coffee Break 30m
    • 4:00 PM 5:00 PM
      Solution of theta-Vacuum and Chemical Potential Sign Problems in CP(N-1) Models Regularized with SU(N) Quantum Spin Ladders 1h
      Speaker: Uwe-Jens Wiese
    • 5:00 PM 7:00 PM
      Poster Session 2h
    • 9:00 AM 10:00 AM
      Deterministic dynamics of initially random systems 1h
      Speaker: Vincent Pasquier
    • 10:00 AM 11:00 AM
      Critical properties of the interacting Majorana chain. The power of Friedel oscillations 1h
      Speaker: Natalia Chepiga
    • 11:00 AM 11:30 AM
      Coffee Break 30m
    • 11:30 AM 12:30 PM
      Does tensor RG converge because of truncation effects? 1h
      Speaker: Slava Rychkov
    • 12:30 PM 2:30 PM
      Lunch Break 2h
    • 2:30 PM 3:30 PM
      Lower bounds on ground state energies from tensor networks 1h
      Speaker: Norbert Schuch
    • 3:30 PM 4:00 PM
      Coffee Break 30m
    • 4:00 PM 5:00 PM
      Finite-Size “Level Spectroscopy” Approach with Tensor Network Renormalization 1h
      Speaker: Masaki Oshikawa
    • 7:30 PM 9:30 PM
      Workshop Dinner Restaurant Le Debarcadere in St. Sulpice 2h

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

    • 9:00 AM 10:00 AM
      Entanglement, symmetries, and asymmetry 1h
      Speaker: Pasquale Calabrese
    • 10:00 AM 11:00 AM
      Investigating thermal critical points with tensor networks 1h
      Speaker: Frederic Mila
    • 11:00 AM 11:30 AM
      Coffee Break 30m
    • 11:30 AM 12:30 PM
      Entanglement entropies for Lifshitz fermionic fields at finite density 1h
      Speaker: Erik Tonni
    • 12:30 PM 2:30 PM
      Lunch Break 2h
    • 2:30 PM 3:30 PM
      Finite-depth scaling of infinite quantum circuits for quantum critical points 1h
      Speaker: Frank Pollmann
    • 3:30 PM 4:00 PM
      Coffee Break 30m
    • 4:00 PM 5:00 PM
      Tensor network algorithms for high-dimensional quantum many-body systems 1h
      Speaker: Simone Montangero
    • 5:00 PM 6:00 PM
      Discussion Session 1h
    • 9:00 AM 10:00 AM
      Tensor Networks Can Resolve Fermi Surfaces 1h
      Speaker: Quinten Mortier
    • 10:00 AM 11:00 AM
      Tensor network approach for 2D chiral spin liquids 1h
      Speaker: Didier Poilblanc
    • 11:00 AM 11:30 AM
      Coffee Break 30m
    • 11:30 AM 12:30 PM
      A scaling hypothesis for PEPS and MPS 1h
      Speaker: Bram Vanhecke
    • 12:30 PM 1:30 PM
      Closing, Lunch and Departure 1h