Many-body quantum chaos: analytic connection to random matrix theory
Kos, Pavel (Avtor), Ljubotina, Marko (Avtor), Prosen, Tomaž (Avtor)

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A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). Most prominent features of such RMT behavior with respect to a random spectrum, both encompassed in the spectral pair correlation function, are statistical suppression of small level spacings (correlation hole) and enhanced stiffness of the spectrum at large spectral ranges. For single-particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry [Proc. R. Soc. A 400, 229 (1985)] within the so-called diagonal approximation of semiclassical periodic-orbit sums, while the derivation of the full RMT spectral form factor K(t) (Fourier transform of the spectral pair correlation function) from semiclassics has been completed by Müller et al. [Phys. Rev. Lett. 93, 014103 (2004)]. In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming to the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behavior which are termed the “many-body localized phase” and “ergodic phase.” In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide a clear theoretical explanation for these observations. We compute K(t) in the leading two orders in t and show its agreement with RMT for nonintegrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin-1/2 models in a periodically kicking transverse field. In particular, we relate K(t) to partition functions of a class of twisted classical Ising models on a ring of size t; hence, the leading-order RMT behavior K(t)≃2t is a consequence of translation and reflection symmetry of the Ising partition function.

Jezik:Angleški jezik
Ključne besede:statistical physics, strongly correlated systems, quantum mechanics, quantum statistical mechanics
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:FMF - Fakulteta za matematiko in fiziko
Leto izida:2018
Št. strani:str. 021062-1-021062-11
Številčenje:Vol. 8, iss. 2
ISSN pri članku:2160-3308
DOI:10.1103/PhysRevX.8.021062 Povezava se odpre v novem oknu
COBISS.SI-ID:3208036 Povezava se odpre v novem oknu
Število ogledov:558
Število prenosov:354
Skupna ocena:(0 glasov)
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Gradivo je del revije

Naslov:Physical review
Skrajšan naslov:Phys. rev., X
Založnik:American Physical Society
COBISS.SI-ID:19686152 Povezava se odpre v novem oknu

Gradivo je financirano iz projekta

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

Sekundarni jezik

Jezik:Slovenski jezik
Ključne besede:statistična fizika, močno korelirani sistemi, kvantna mehanika, kvantna statistična mehanika

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