Universal dynamical phase diagram of lattice spin models and strongly correlated ultracold atoms in optical lattices

TL;DR

This paper develops a universal dynamical phase diagram for lattice spin models and ultracold atoms, revealing regimes characterized by solitonic excitations and their stability, with implications for experimental ultracold atom systems.

Contribution

It introduces a universal phase diagram for anisotropic Heisenberg models based on soliton properties and stability, combining analytical and numerical methods.

Findings

Identification of distinct dynamical regimes based on soliton behavior

Analytical mapping to KdV equations for small perturbations

Numerical confirmation of soliton properties at large amplitudes

Abstract

We study semiclassical dynamics of anisotropic Heisenberg models in two and three dimensions. Such models describe lattice spin systems and hard core bosons in optical lattices. We solve numerically Landau-Lifshitz type equations on a lattice and show that in the phase diagram of magnetization and interaction anisotropy, one can identify several distinct regimes of dynamics. These regions can be distinguished based on the character of one dimensional solitonic excitations, and stability of such solitons to transverse modulation. Small amplitude and long wavelength perturbations can be analyzed analytically using mapping of non-linear hydrodynamic equations to KdV type equations. Numerically we find that properties of solitons and dynamics in general remain similar to our analytical results even for large amplitude and short distance inhomogeneities, which allows us to obtain a universal dynamical phase diagram. As a concrete example we study dynamical evolution of the system starting from a state with magnetization step and show that formation of oscillatory regions and their stability to transverse modulation can be understood from the properties of solitons. In regimes unstable to transverse modulation we observe formation of lump type solutions with modulation in all directions. We discuss implications of our results for experiments with ultracold atoms.