Exact spectral form factor in a minimal model of many-body quantum chaos
ID Bertini, Bruno (Author), ID Kos, Pavel (Author), ID Prosen, Tomaž (Author)

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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.

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
Number of pages:Str. 264101-1-264101-6
Numbering:Vol. 121, iss. 26
PID:20.500.12556/RUL-105985 This link opens in a new window
ISSN on article:0031-9007
DOI:10.1103/PhysRevLett.121.264101 This link opens in a new window
COBISS.SI-ID:3285604 This link opens in a new window
Publication date in RUL:10.01.2019
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Record is a part of a journal

Title:Physical review letters
Shortened title:Phys. rev. lett.
Publisher:American Physical Society
COBISS.SI-ID:1282575 This link opens in a new window

Secondary language

Keywords:kvantna mehanika, kvantni kaos, statistična fizika


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

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