Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice
ID Krajnik, Žiga (Author), ID Prosen, Tomaž (Author)

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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:statistical physics, integrable systems, spin chains, spin transport
Typology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Publication status in journal:Published
Article version:Postprint, final article version, accepted into publication
Number of pages:Str. 110-130
Numbering:Vol. 179, iss. 1
PID:20.500.12556/RUL-117822 This link opens in a new window
ISSN on article:0022-4715
DOI:10.1007/s10955-020-02523-1 This link opens in a new window
COBISS.SI-ID:23775747 This link opens in a new window
Publication date in RUL:29.07.2020
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Record is a part of a journal

Title:Journal of statistical physics
Shortened title:J. stat. phys.
Publisher:Plenum Press.
COBISS.SI-ID:25793280 This link opens in a new window

Secondary language

Keywords:statistična fizika, integrabilni sistemi, spinske verige, spinski transport


Funder:EC - European Commission
Funding programme:H2020
Project number:694544
Name:Open Many-body Non-Equilibrium Systems

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
Project number:P1-0402
Name:Matematična fizika

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