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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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MD5: 839C3377544DC68B596B41E25B336351
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https://link.springer.com/article/10.1007/s10955-020-02523-1
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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.
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
Views:
1066
Downloads:
415
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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
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