Structural stability hypothesis of dual unitary quantum chaos

Riddell, Jonathon (author), Keyserlingk, Curt von (author), Prosen, Tomaž (author), Bertini, Bruno (author)

Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any semiclassical limit. Although this property is extremely difficult to prove analytically for generic many-body systems, a rigorous proof has been achieved for dual-unitary circuits—a special class of local quantum circuits that remain unitary upon swapping space and time. Here we consider the fate of this property when moving from dual-unitary to generic quantum circuits focusing on the spectral form factor, i.e., the Fourier transform of the two-point correlation. We begin with a numerical survey that, in agreement with previous studies, suggests that there exists a finite region in parameter space where dual-unitary physics is stable and spectral correlations are still described by random matrix theory, although up to a maximal quasienergy scale. To explain these findings, we develop a perturbative expansion: it recovers the random matrix theory predictions, provided the terms occurring in perturbation theory obey a relatively simple set of assumptions. We then provide numerical evidence and a heuristic analytical argument supporting these assumptions.

• Language: English
• Keywords: quantum chaos, quantum many-body systems, quantum physics, statistical physics
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: Str. 033226-1-033226-21
• Numbering: Vol. 6, iss. 3
• PID: 20.500.12556/RUL-168179
• UDC: 530.145
• ISSN on article: 2643-1564
• DOI: 10.1103/PhysRevResearch.6.033226
• COBISS.SI-ID: 231006723
• Publication date in RUL: 01.04.2025

Record is a part of a journal

• Title: Physical review research
• Publisher: American Phyisical Society
• ISSN: 2643-1564
• COBISS.SI-ID: 32822823

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: kvantni kaos, kvantni večdelčni sistemi, kvantna fizika, statistična fizika