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Extracting the symmetries of nonequilibrium quantum many-body systems

by Aleksandr N. Mikheev, Viktoria Noel, Ido Siovitz, Helmut Strobel, Markus K. Oberthaler, Jürgen Berges

Submission summary

Authors (as registered SciPost users): Aleksandr Mikheev · Viktoria Noel
Submission information
Preprint Link: https://arxiv.org/abs/2407.17913v2  (pdf)
Date accepted: 2024-12-27
Date submitted: 2024-12-03 10:40
Submitted by: Mikheev, Aleksandr
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Atomic, Molecular and Optical Physics - Experiment
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approaches: Theoretical, Experimental, Computational

Abstract

Symmetries play a pivotal role in our understanding of the properties of quantum many-body systems. While there are theorems and a well-established toolbox for systems in thermal equilibrium, much less is known about the role of symmetries and their connection to dynamics out of equilibrium. This arises due to the direct link between a system's thermal state and its Hamiltonian, which is generally not the case for nonequilibrium dynamics. Here we present a pathway to identify the effective symmetries and to extract them from data in nonequilibrium quantum many-body systems. Our approach is based on exact relations between correlation functions involving different numbers of spatial points, which can be viewed as nonequilibrium versions of (equal-time) Ward identities encoding the symmetries of the system. We derive symmetry witnesses, which are particularly suitable for the analysis of measured or simulated data at different snapshots in time. To demonstrate the potential of the approach, we apply our method to numerical and experimental data for a spinor Bose gas. We investigate the important question of a dynamical restoration of an explicitly broken symmetry of the Hamiltonian by the initial state. Remarkably, it is found that effective symmetry restoration can occur long before the system equilibrates. We also use the approach to define and identify spontaneous symmetry breaking far from equilibrium, which is of great relevance for applications to nonequilibrium phase transitions. Our work opens new avenues for the classification and analysis of quantum as well as classical many-body dynamics in a large variety of systems, ranging from ultracold quantum gases to cosmology.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block

Author comments upon resubmission

Dear Editor,

We would like to thank the referees for their insightful reports. We provide a detailed response to their feedback in the replies below the reports. We hope that the revised version of our manuscript is suitable for publication in SciPost Physics.

List of changes

* Added references in the introduction.
* Added more clarity and details in Sec. III and App. A regarding the experiment and how measurements were obtained.
* Added more steps in the derivation between Eqs. (12)-(20) in Sec. IV.
* Added a discussion at the end of Sec. IV regarding the experimental connection.
* Revised the discussion of the interpretation of symmetry witnesses according to the comments of Referee #2 in Sec. V.
* Expanded on the discussion of potential applications at the end of Sec. VII.

Current status:
Accepted in target Journal

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)


Reports on this Submission

Report #2 by Anonymous (Referee 1) on 2024-12-18 (Invited Report)

Report

The authors have taken into account all my comments and made
corresponding changes in the main text.
I recommend the publication in SciPost Physics.

Recommendation

Publish (easily meets expectations and criteria for this Journal; among top 50%)

  • validity: top
  • significance: top
  • originality: top
  • clarity: top
  • formatting: perfect
  • grammar: perfect

Report #1 by Anonymous (Referee 2) on 2024-12-12 (Invited Report)

Report

The authors have addressed all concerns raised in my earlier report. With the added remarks I believe that there is no ambiguity about the interpretation of the symmetry witnesses. I recommend publication of the manuscript in its present form.

Recommendation

Publish (easily meets expectations and criteria for this Journal; among top 50%)

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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