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Dual symplectic classical circuits: An exactly solvable model of many-body chaos

by Alexios Christopoulos, Andrea De Luca, D L Kovrizhin, Tomaž Prosen

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Submission summary

Authors (as registered SciPost users): Alexios Christopoulos
Submission information
Preprint Link: scipost_202307_00022v2  (pdf)
Date accepted: 2024-01-31
Date submitted: 2023-11-27 20:06
Submitted by: Christopoulos, Alexios
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
Approaches: Theoretical, Computational

Abstract

We propose a general exact method of calculating dynamical correlation functions in dual symplectic brick-wall circuits in one dimension. These are deterministic classical many-body dynamical systems which can be interpreted in terms of symplectic dynamics in two orthogonal (time and space) directions. In close analogy with quantum dual-unitary circuits, we prove that two-point dynamical correlation functions are non-vanishing only along the edges of the light cones. The dynamical correlations are exactly computable in terms of a one-site Markov transfer operator, which is generally of infinite dimensionality. We test our theory in a specific family of dual-symplectic circuits, describing the dynamics of a classical Floquet spin chain. Remarkably, expressing these models in the form of a composition of rotations leads to a transfer operator with a block diagonal form in the basis of spherical harmonics. This allows us to obtain analytical predictions for simple local observables. We demonstrate the validity of our theory by comparison with Monte Carlo simulations, displaying excellent agreement with the latter for different choices of observables.

Published as SciPost Phys. 16, 049 (2024)



Author comments upon resubmission

Dear editor,

Herewith we resubmit our manuscript titled “Dual symplectic classical circuits: An exactly solvable model of many-body chaos” to SciPost. We would like to express our gratitude to the reviewers for their time and their invaluable feedback on the initial submission. In response to their constructive comments, we have made improvements to our work, enhancing its scientific rigour and
clarity. Please see our response below.

Yours sincerely,

Alexios Christopoulos (on behalf of all coauthors)

For more details regarding the changes made to the manuscript and the replies to the reviewers, please refer to the attached PDF as a response to the reviewers' comments.

List of changes

For more details regarding the changes made to the manuscript and the replies to the reviewers, please refer to the attached PDF as a response to the reviewers' comments.


Reports on this Submission

Anonymous Report 3 on 2023-11-29 (Invited Report)

Report

I am happy with the revised version which in my view can be published as is.

  • validity: top
  • significance: top
  • originality: top
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Report 2 by Pieter W. Claeys on 2023-11-28 (Invited Report)

Report

All my questions and comments have been appropriately addressed and I am happy to recommend this paper for publication in SciPost Physics.

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

Anonymous Report 1 on 2023-11-27 (Invited Report)

Report

The authors have addressed my comments fully, and I thus recommend publication of the manuscript.

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

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Comments

Anonymous on 2023-11-28  [id 4153]

See the attached document for the changes to the manuscript and answers to the reviewers.

Attachment:

resubmission_letter.pdf