Exact spectral form factor in a minimal model of many-body quantum chaos

Bertini, Bruno (author), Kos, Pavel (author), Prosen, Tomaž (author)

The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well-defined classical limit as well as by systems with no classical correspondence, such as locally interacting spins or fermions. Despite great phenomenological success, a general mechanism explaining the emergence of RMT without reference to semiclassical concepts is still missing. Here we provide the example of a quantum many-body system with no semiclassical limit (no large parameter) where the emergence of RMT spectral correlations is proven exactly. Specifically, we consider a periodically driven Ising model and write the Fourier transform of spectral density’s two-point function, the spectral form factor, in terms of a partition function of a two-dimensional classical Ising model featuring a space-time duality. We show that the self-dual cases provide a minimal model of many-body quantum chaos, where the spectral form factor is demonstrated to match RMT for all values of the integer time variable t in the thermodynamic limit. In particular, we rigorously prove RMT form factor for an odd t, while we formulate a precise conjecture for an even t. The results imply ergodicity for any finite amount of disorder in the longitudinal field, rigorously excluding the possibility of many-body localization. Our method provides a novel route for obtaining exact nonperturbative results in nonintegrable systems.

• Language: English
• Keywords: quantum mechanics, quantum chaos, statistical physics
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2018
• Number of pages: Str. 264101-1-264101-6
• Numbering: Vol. 121, iss. 26
• PID: 20.500.12556/RUL-105985
• UDC: 530.145
• ISSN on article: 0031-9007
• DOI: 10.1103/PhysRevLett.121.264101
• COBISS.SI-ID: 3285604
• Publication date in RUL: 10.01.2019

Record is a part of a journal

• Title: Physical review letters
• Shortened title: Phys. rev. lett.
• Publisher: American Physical Society
• ISSN: 0031-9007
• COBISS.SI-ID: 1282575

Secondary language

• Language: Slovenian
• Keywords: kvantna mehanika, kvantni kaos, statistična fizika

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open many-body non-equilibrium systems
• Acronym: OMNES