Many-body quantum chaos and dual-unitarity round-a-face

Prosen, Tomaž (avtor)

We propose a new type of locally interacting quantum circuits—quantum cellular automata—that are generated by unitary interactions round-a-face (IRF). Specifically, we discuss a set (or manifold) of dual-unitary IRFs with local Hilbert space dimension d [DUIRF(d)], which generate unitary evolutions both in space and time directions of an extended 1+1 dimensional lattice. We show how arbitrary dynamical correlation functions of local observables can be evaluated in terms of finite-dimensional completely positive trace preserving unital maps in complete analogy to recently studied circuits made of dual-unitary brick gates (DUBGs). The simplest non-vanishing local correlation functions in dual-unitary IRF circuits are shown to involve observables non-trivially supported on two neighboring sites. We completely characterize the ten-dimensional manifold of DUIRF(2) for qubits (d = 2) and provide, for d = 3,4,...,7, empirical estimates of its dimensionality based on numerically determined dimensions of tangent spaces at an ensemble of random instances of dual-unitary IRF gates. In parallel, we apply the same algorithm to determine dimDUBG(d) and show that they are of similar order though systematically larger than dimDUIRF(d) for d = 2,3,...,7. It is remarkable that both sets have a rather complex topology for d ≥ 3 in the sense that the dimension of the tangent space varies among different randomly generated points of the set. Finally, we provide additional data on dimensionality of the chiral extension of DUBG circuits with distinct local Hilbert spaces of dimensions d ̸= d′ residing at even/odd lattice sites.

• Jezik: Angleški jezik
• Ključne besede: quantum chaos
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Recenzirani rokopis
• Leto izida: 2021
• Št. strani: Str. 093101-1-093101-11
• Številčenje: Vol. 31, iss. 9
• PID: 20.500.12556/RUL-130297
• UDK: 530.145
• ISSN pri članku: 1054-1500
• DOI: 10.1063/5.0056970
• COBISS.SI-ID: 76100867
• Datum objave v RUL: 13.09.2021

Gradivo je del revije

• Naslov: Chaos
• Skrajšan naslov: Chaos
• Založnik: American Institute of Physics
• ISSN: 1054-1500
• COBISS.SI-ID: 2800167

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: kvantni kaos

Projekti

• Financer: EC - European Commission
• Program financ.: H2020
• Številka projekta: 694544
• Naslov: Open Many-body Non-Equilibrium Systems
• Akronim: OMNES

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P1-0402
• Naslov: Matematična fizika