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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)

  • Monday 28 November
    • 1
      Symmetric PEPS analysis of a phase transition in coupled spin-1/2 ladders
      Speaker: Juraj Hasik
      Hasik.pdf
    • 11:00
      Coffee Break
    • 2
      Open issues on finite entanglement scaling, the case of the transfer matrix spectrum
      Speaker: Luca Tagliacozzo
      Tagliacozzo.pdf
    • 12:30
      Lunch Break
    • 3
      Defects, Duality and Categorical Symmetries
      Speaker: Paul Fendley
      Fendley.pdf
    • 15:30
      Coffee Break
    • 4
      Relativistic matrix product states and an application to the Sinh-Gordon model
      Speaker: Antoine Tilloy
      Tilloy.pdf
  • Tuesday 29 November
    • 5
      Light cone tensor network and time evolution
      Speaker: Mari-Carmen Banuls
      Banuls.pdf
    • 6
      Peculiarities of RG flows in 2d O(n) models
      Speaker: Victor Gorbenko
      Gorbenko.pdf
    • 11:00
      Coffee Break
    • 7
      Torus spectroscopy of quantum critical points: A fingerprint of higher-dimension conformal field theories
      Speaker: Michael Schuler
      Schuler.pdf
    • 12:30
      Lunch Break
    • 8
      Applications of finite correlation length scaling with iPEPS
      Speaker: Philippe Corboz
      Corboz.pdf
    • 15:30
      Coffee Break
    • 9
      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
    • 10
      Poster Session
  • Wednesday 30 November
    • 11
      Deterministic dynamics of initially random systems
      Speaker: Vincent Pasquier
      Pasquier.pdf
    • 12
      Critical properties of the interacting Majorana chain. The power of Friedel oscillations
      Speaker: Natalia Chepiga
      Chepiga.pdf
    • 11:00
      Coffee Break
    • 13
      Does tensor RG converge because of truncation effects?
      Speaker: Slava Rychkov
    • 12:30
      Lunch Break
    • 14
      Lower bounds on ground state energies from tensor networks
      Speaker: Norbert Schuch
    • 15:30
      Coffee Break
    • 15
      Finite-Size “Level Spectroscopy” Approach with Tensor Network Renormalization
      Speaker: Masaki Oshikawa
      Oshikawa.pdf
    • 19:30
      Workshop Dinner Restaurant Le Debarcadere in St. Sulpice

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

  • Thursday 1 December
    • 16
      Entanglement, symmetries, and asymmetry
      Speaker: Pasquale Calabrese
      Calabrese.pdf
    • 17
      Investigating thermal critical points with tensor networks
      Speaker: Frederic Mila
      Mila.pdf
    • 11:00
      Coffee Break
    • 18
      Entanglement entropies for Lifshitz fermionic fields at finite density
      Speaker: Erik Tonni
    • 12:30
      Lunch Break
    • 19
      Finite-depth scaling of infinite quantum circuits for quantum critical points
      Speaker: Frank Pollmann
      Pollmann.pdf
    • 15:30
      Coffee Break
    • 20
      Tensor network algorithms for high-dimensional quantum many-body systems
      Speaker: Simone Montangero
    • 21
      Discussion Session
  • Friday 2 December
    • 22
      Tensor Networks Can Resolve Fermi Surfaces
      Speaker: Quinten Mortier
      Mortier.pdf
    • 23
      Tensor network approach for 2D chiral spin liquids
      Speaker: Didier Poilblanc
    • 11:00
      Coffee Break
    • 24
      A scaling hypothesis for PEPS and MPS
      Speaker: Bram Vanhecke
      Vanhecke.pdf
    • 12:30
      Closing, Lunch and Departure
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