Anisotropic Landau-Lifshitz Model in Discrete Space-Time

TL;DR

This paper develops an integrable discrete space-time model of classical spins with anisotropy, enabling analysis of spin transport properties and revealing different regimes including superdiffusion near isotropy.

Contribution

It introduces a novel discrete integrable lattice model of anisotropic Landau-Lifshitz spins and applies it to compute transport coefficients.

Findings

Different behaviors in easy-axis and easy-plane regimes

Algebraic divergence of diffusion constant near isotropic point

Evidence of spin superdiffusion crossover

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.