Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice

Krajnik, Žiga (avtor), Prosen, Tomaž (avtor)

We introduce a deterministic SO(3) invariant dynamics of classical spins on a discrete space–time lattice and prove its complete integrability by explicitly finding a related non-constant (baxterized) solution of the set-theoretic Yang–Baxter equation over the 2-sphere. Equipping the algebraic structure with the corresponding Lax operator we derive an infinite sequence of conserved quantities with local densities. The dynamics depend on a single continuous spectral parameter and reduce to a (lattice) Landau–Lifshitz model in the limit of a small parameter which corresponds to the continuous time limit. Using quasi-exact numerical simulations of deterministic dynamics and Monte Carlo sampling of initial conditions corresponding to a maximum entropy equilibrium state we determine spin-spin spatio-temporal (dynamical) correlation functions with relative accuracy of three orders of magnitude. We demonstrate that in the equilibrium state with a vanishing total magnetization the correlation function precisely follows Kardar–Parisi–Zhang scaling hence the spin transport belongs to the universality class with dynamical exponent z=3/2, in accordance to recent related simulations in discrete and continuous time quantum Heisenberg spin 1/2 chains.

• Jezik: Angleški jezik
• Ključne besede: statistical physics, integrable systems, spin chains, spin transport
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Recenzirani rokopis
• Leto izida: 2020
• Št. strani: Str. 110-130
• Številčenje: Vol. 179, iss. 1
• PID: 20.500.12556/RUL-117822
• UDK: 536.9
• ISSN pri članku: 0022-4715
• DOI: 10.1007/s10955-020-02523-1
• COBISS.SI-ID: 23775747
• Datum objave v RUL: 29.07.2020

Gradivo je del revije

• Naslov: Journal of statistical physics
• Skrajšan naslov: J. stat. phys.
• Založnik: Plenum Press.
• ISSN: 0022-4715
• COBISS.SI-ID: 25793280

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: statistična fizika, integrabilni sistemi, spinske verige, spinski transport

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