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

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Izvleček
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.

Jezik:Angleški jezik
Ključne besede:quantum mechanics, quantum chaos, statistical physics
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:FMF - Fakulteta za matematiko in fiziko
Status publikacije:Objavljeno
Različica publikacije:Recenzirani rokopis
Leto izida:2018
Št. strani:Str. 264101-1-264101-6
Številčenje:Vol. 121, iss. 26
PID:20.500.12556/RUL-105985 Povezava se odpre v novem oknu
UDK:530.145
ISSN pri članku:0031-9007
DOI:10.1103/PhysRevLett.121.264101 Povezava se odpre v novem oknu
COBISS.SI-ID:3285604 Povezava se odpre v novem oknu
Datum objave v RUL:10.01.2019
Število ogledov:1660
Število prenosov:841
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Gradivo je del revije

Naslov:Physical review letters
Skrajšan naslov:Phys. rev. lett.
Založnik:American Physical Society
ISSN:0031-9007
COBISS.SI-ID:1282575 Povezava se odpre v novem oknu

Sekundarni jezik

Jezik:Slovenski jezik
Ključne besede:kvantna mehanika, kvantni kaos, statistična fizika

Projekti

Financer:EC - European Commission
Program financ.:H2020
Številka projekta:694544
Naslov:Open many-body non-equilibrium systems
Akronim:OMNES

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