Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice
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.
2020
2020-07-29 07:49:31
1033
statistical physics, integrable systems, spin chains, spin transport
statistična fizika, integrabilni sistemi, spinske verige, spinski transport
Žiga
Krajnik
70
Tomaž
Prosen
70
UDK
4
536.9
ISSN pri članku
9
0022-4715
DOI
15
10.1007/s10955-020-02523-1
COBISS_ID
3
23775747
OceCobissID
13
25793280
RAZ_Krajnik_Ziga_2020.pdf
2147662
Predstavitvena datoteka
2020-07-29 07:54:11
0
Izvorni URL
2021-02-12 13:06:49