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

Krajnik, Žiga (author), Prosen, Tomaž (author)

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.

• Language: English
• Keywords: statistical physics, integrable systems, spin chains, spin transport
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2020
• Number of pages: Str. 110-130
• Numbering: Vol. 179, iss. 1
• PID: 20.500.12556/RUL-117822
• UDC: 536.9
• ISSN on article: 0022-4715
• DOI: 10.1007/s10955-020-02523-1
• COBISS.SI-ID: 23775747
• Publication date in RUL: 29.07.2020

Record is a part of a journal

• Title: Journal of statistical physics
• Shortened title: J. stat. phys.
• Publisher: Plenum Press.
• ISSN: 0022-4715
• COBISS.SI-ID: 25793280

Secondary language

• Language: Slovenian
• Keywords: statistična fizika, integrabilni sistemi, spinske verige, spinski transport

Projects

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

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika