Semiclassical dynamics of spin density waves

TL;DR

This paper develops a semiclassical simulation framework for spin-density-wave dynamics, enabling large-scale real-space studies of SDW behavior and responses at finite temperatures.

Contribution

It introduces a quantum Landau-Lifshitz dynamics method that combines a semiclassical approximation with an enhanced kernel polynomial approach for large-scale SDW simulations.

Findings

Able to simulate SDW dynamics on ~10^5 sites

Computed dynamical responses of complex SDW configurations

Showed importance of spatial correlations in SDW relaxation

Abstract

We present a theoretical framework for equilibrium and nonequilibrium dynamical simulation of quantum states with spin-density-wave (SDW) order. Within a semiclassical adiabatic approximation that retains electron degrees of freedom, we demonstrate that the SDW order parameter obeys a generalized Landau-Lifshitz equation. With the aid of an enhanced kernel polynomial method, our linear-scaling quantum Landau-Lifshitz dynamics (QLLD) method enables dynamical SDW simulations with $N \simeq 10^5$ lattice sites. Our real-space formulation can be used to compute dynamical responses, such as dynamical structure factor, of complex and even inhomogeneous SDW configurations at zero or finite temperatures. Applying the QLLD to study the relaxation of a noncoplanar topological SDW under the excitation of a short pulse, we further demonstrate the crucial role of spatial correlations and fluctuations in the SDW dynamics.