Exact spectral form factor in a minimal model of many-body quantum chaos
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.
2018
2019-01-10 10:10:40
1033
quantum mechanics, quantum chaos, statistical physics
kvantna mehanika, kvantni kaos, statistična fizika
Bruno
Bertini
70
Pavel
Kos
70
Tomaž
Prosen
70
UDK
4
530.145
ISSN pri članku
9
0031-9007
DOI
15
10.1103/PhysRevLett.121.264101
COBISS_ID
3
3285604
OceCobissID
13
1282575
RAZ_Bertini_Bruno_i2018.pdf
940801
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2019-01-10 10:13:02
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2021-02-12 14:34:38