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On computing non-equilibrium dynamics following a quench

by Neil J. Robinson, Albertus J. J. M. de Klerk, Jean-Sébastien Caux

This Submission thread is now published as

Submission summary

As Contributors: Neil Robinson · Albertus de Klerk
Arxiv Link: (pdf)
Code repository:
Date accepted: 2021-09-17
Date submitted: 2021-09-07 11:35
Submitted by: de Klerk, Albertus
Submitted to: SciPost Physics
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


Computing the non-equilibrium dynamics that follows a quantum quench is difficult, even in exactly solvable models. Results are often predicated on the ability to compute overlaps between the initial state and eigenstates of the Hamiltonian that governs time evolution. Except for a handful of known cases, it is generically not possible to find these overlaps analytically. Here we develop a numerical approach to preferentially generate the states with high overlaps for a quantum quench starting from the ground state or an excited state of an initial Hamiltonian. We use these preferentially generated states, in combination with a "high overlap states truncation scheme" and a modification of the numerical renormalization group, to compute non-equilibrium dynamics following a quench in the Lieb-Liniger model. The method is non-perturbative, works for reasonable numbers of particles, and applies to both continuum and lattice systems. It can also be easily extended to more complicated scenarios, including those with integrability breaking.

Published as SciPost Phys. 11, 104 (2021)

Author comments upon resubmission

With this resubmission we hope to clear up any misunderstanding there was regarding the computation of the entanglement entropy between us and the first referee.

List of changes

To address the response of referee number one to our changes we have modified our comment in the conclusions regarding the computation of the entanglement entropy to the following:

"Finally, we would like to point out that the method developed in this paper provides, in principle, all the ingredients necessary to compute for example the time evolution of the entanglement entropy. In order to come to a tractable computation one can convert the overlaps coming from the NRG-routines to a root distribution and then use the quasi-particle picture formulas for the entanglement entropy, see e.g. \cite{calabrese_evolution_2005,alba_entanglement_2018}. However, in order to ascertain the accuracy of results obtained in this way, a careful quantitative study of finite-size effects is required in order to determine if we can accurately match results in the thermodynamic and scaling limits. We leave addressing this challenge to future work."

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