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

Christopoulos, Alexios (author), De Luca, Andrea (author), Kovrizhin, Dmitry L. (author), Prosen, Tomaž (author)

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 a choice of observables.

• Language: English
• Keywords: dynamical systems, chaos, statistical mechanics, quantum mechanics
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication version: Version of Record
• Publication date: 20.02.2024
• Year: 2024
• Number of pages: 23 str.
• Numbering: Vol. 16, iss. 2, art. no. 049
• PID: 20.500.12556/RUL-155477
• UDC: 530.182
• ISSN on article: 2542-4653
• DOI: 10.21468/SciPostPhys.16.2.049
• COBISS.SI-ID: 191320067
• Publication date in RUL: 04.04.2024

Record is a part of a journal

• Title: SciPost physics
• Publisher: SciPost Foundation
• ISSN: 2542-4653
• COBISS.SI-ID: 526154521

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: dinamični sistemi, kaos, statistična mehanika, kvantna mehanika