Anisotropic Landau-Lifshitz Model in Discrete Space-Time

Abstract

We construct an integrable lattice model of classical interacting spins in discrete space-time, representing a discrete-time analogue of the lattice Landau-Lifshitz ferromagnet with uniaxial anisotropy. As an application we use this explicit discrete symplectic integration scheme to compute the spin Drude weight and diffusion constant as functions of anisotropy and chemical potential. We demonstrate qualitatively different behavior in the easy-axis and the easy-plane regimes in the non-magnetized sector. Upon approaching the isotropic point we also find an algebraic divergence of the diffusion constant, signaling a crossover to spin superdiffusion.

20 pages, 9 figures; V2: typos corrected, a few DOIs added; V3: mistake in Eq. (2.20) corrected, V4: Corrected typo in Eq. (2.43) - primes in (2, 2) matrix element swapped

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• Absence of Normal Fluctuations in an Integrable Magnet
• Anomalous transport from hot quasiparticles in interacting spin chains
• Dynamical criticality of magnetization transfer in integrable spin chains
• The Floquet Baxterisation
• Popcorn Drude weights from quantum symmetry
• Current correlations, Drude weights and large deviations in a box-ball system
• Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains
• Landau-Lifschitz magnets: exact thermodynamics and transport
• Quantum many-body spin ratchets
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Local integrability breaking and exponential localization of leading Lyapunov vectors
• Integrable fishnet circuits and Brownian solitons