Žiga Krajnik (Author), Tomaž Prosen (Author)

Abstract

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.

Keywords

statistična fizika;integrabilni sistemi;spinske verige;spinski transport;statistical physics;integrable systems;spin chains;spin transport;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 536.9
COBISS: 23775747 Link will open in a new window
ISSN: 0022-4715
Views: 410
Downloads: 160
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Other data

Secondary language: Slovenian
Secondary keywords: statistična fizika;integrabilni sistemi;spinske verige;spinski transport;
Pages: str. 110-130
Volume: ǂVol. ǂ179
Issue: ǂiss. ǂ1
Chronology: 2020
DOI: 10.1007/s10955-020-02523-1
ID: 11924498