Semiclassical description of Heisenberg models via spin-coherent states

TL;DR

This paper develops a semiclassical framework for Heisenberg models using spin-coherent states, enabling analysis of quantum fluctuations and applications to solitons, instantons, and vortices in low-dimensional systems.

Contribution

It introduces a novel semiclassical approach with a variance measure for quantum fluctuations, extending the analysis of Heisenberg models beyond traditional methods.

Findings

Variance of Hamiltonian relates to quantum fluctuations.

Application to solitons, instantons, vortices in 1D and 2D models.

Provides a natural interpretation of time-dependent solutions.

Abstract

We use spin-coherent states as a time-dependent variational ansatz for a semiclassical description of a large family of Heisenberg models. In addition to common approaches we also evaluate the square variance of the Hamiltonian in terms of coherent states. This quantity turns out to have a natural interpretation with respect to time-dependent solutions of the equations of motion and allows for an estimate of quantum fluctuations in a semiclassical regime. The general results are applied to solitons, instantons and vortices in several one- and two-dimensional models.