Exact spectral form factor in a minimal model of many-body quantum chaos

Bertini, Bruno (avtor), Kos, Pavel (avtor), Prosen, Tomaž (avtor)

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
• UDK: 530.145
• ISSN pri članku: 0031-9007
• DOI: 10.1103/PhysRevLett.121.264101
• COBISS.SI-ID: 3285604
• Datum objave v RUL: 10.01.2019

Gradivo je del revije

• Naslov: Physical review letters
• Skrajšan naslov: Phys. rev. lett.
• Založnik: American Physical Society
• ISSN: 0031-9007
• COBISS.SI-ID: 1282575

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