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

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Abstract
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
Tipology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Year:2018
Number of pages:str. 264101-1-264101-6
Numbering:Vol. 121, iss. 26
UDC:530.145
ISSN on article:0031-9007
DOI:10.1103/PhysRevLett.121.264101 Link is opened in a new window
COBISS.SI-ID:3285604 Link is opened in a new window
Views:753
Downloads:333
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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 This link opens in a new window

Document is financed by a project

Funder:EC - European Commission
Funding Programme:H2020
Project no.:694544
Name:Open many-body non-equilibrium systems
Acronym:OMNES

Secondary language

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

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