Variational Approaches for quantum matter in and out of equilibrium

This school shall introduce PhD students and junior postdoctoral fellows to
advanced numerical techniques, aimed at tackling the physics of quantum
many-body systems in and out-of equilibrium. The focus will be on the
application of state-of-the-art variational approaches to problems emerging in
condensed matter physics, quantum simulation and quantum computing. 


The last ten years have experienced an impressive progress in the level of
precision and control reached in quantum simulators of quantum many-body
physics (based e.g. on ultracold atoms, trapped ions, superconducting circuits,
to cite the most relevant platforms), as well as in spectroscopic and transport
measurements on bulk quantum materials. Hand-in-hand, increasingly
sophisticated theoretical and computational tools have been developed in order
to be able to describe quantitatively equilibrium as well as time-dependent
phenomena in quantum many-body systems. At the same time, the
fundamental question raises whether quantum devices may soon reach – or
have already reached – a long-sought form of “computational advantage” with
respect to their classical counterparts.

Computing equilibrium properties or even non-equilibrium dynamics of a
general, interacting quantum many-body system is an extremely challenging
computational task, with broad applications in moderns physics. In this school
we will focus on selected model systems realized by quantum simulators or
(bulk) condensed matter systems. In particular we want to address
fundamental topics related to time-dependent driven and dissipative systems,
2entanglement dynamics, and complex equilibrium properties of strongly
correlated quantum systems. In this context, a universal numerical strategy in
order to compute the dynamics of a quantum system is based on a clever
variational Ansatz on the quantum state, motivated by physical considerations
as well as by quantum-information insights. Hence our choice of variational
approaches as the overarching theme of this school.

On the methodological side, the school aims at introducing computational tools
which bridge the gap between (under)graduate numerical courses and state-
of-the-art techniques needed to address dynamical phenomena in closed or
open quantum systems. In the main courses we plan to provide detailed
descriptions of the variety of variational methods used in this context (in a
broad sense), and, importantly, also practical examples based on small codes.
A non-exhaustive list of computational methods addressed by the school
include tensor-network states, variational Monte Carlo methods, semiclassical
phase-space approaches, and machine learning techniques. More specialized
techniques, practical applications and experimental results will be illustrated by
invited seminars.



  • Cécile Repellin
    (LPMMC,CNRS & UGA Grenoble)
  • Tommaso Roscilde
    (ENS, Lyon)
  • Markus Holzmann
    (LPMMC, CNRS & UGA Grenoble)


  • Thomas Ayral
  • Mari-Carmen Bañuls
  • Frederico Becca
  • Natalia Chepiga
  • Markus Heyl
  • Anna Keselman
  • Herviou Loïc
  • Julian Leonard
  • Manon Michel
  • Frank Pollmann
  • Davide Rossini
  • Johannes Schachenmayer
  • Marco Schiro
  • Filippo Vicentini
  • Xavier Waintal
  • + TBA


Administrative Coordination

  • Elsa Glasson
  • Marina Riveron
  • Isabel Lelievre

Technical support

  • Mathieu Istas (LPMMC, Grenoble)
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