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.
Highlights
The advent of powerful computational tools [1, 2] has tremendously advanced our understanding of many-body physics in and out of equilibrium [3,4,5,6]
We demonstrate the utility of the constructed dynamical system by studying magnetization transport in thermal equilibrium
We focus on a numerical computation of the linear transport coefficients that quantify magnetization transport on a large spatio-temporal scale, namely the spin Drude weight and the spin diffusion constant
Summary
The advent of powerful computational tools [1, 2] has tremendously advanced our understanding of many-body physics in and out of equilibrium [3,4,5,6]. The study of nonequilibrium properties in classical integrable dynamical systems of interacting particles or fields has received comparatively less attention [44,45,46,47,48,49,50,51]. In addition statistical field theories are commonly plagued by UV divergences (even when the local target space is a compact manifold) These drawbacks can both be obviated in a fully discrete setting. Integrable many-body dynamical systems in discrete time [52, 53] and classical cellular automata [42, 54] have recently attracted much interest. We introduce a discrete zero-curvature property of an auxiliary linear transport problem on a (tilted, light-cone) space-time lattice and interpret it in terms of a local dynamical map acting on a pair of classical spins.
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