Study of Staggered Magnetization in the Spin-$S$ Square-Lattice Heisenberg Model Using Spiral Boundary Conditions

TL;DR

This paper introduces a new numerical approach using spiral boundary conditions to accurately compute local order parameters, like staggered magnetization, in two-dimensional spin systems across various spin values, validated against established methods.

Contribution

The authors develop and validate a novel numerical method employing spiral boundary conditions to determine local order parameters in 2D spin systems for multiple spin values.

Findings

Accurate estimation of staggered magnetization for $S=1/2$ XXZ Heisenberg model.

Extension of the method to higher spins from $S=1$ to $S=6$.

Validation of results through series expansion and spin-wave theory.

Abstract

We propose an efficient numerical method to obtain local order parameter in two-dimensional systems using spiral boundary conditions. As a benchmark, we first estimate the magnitude of staggered magnetization for the $S=1/2$ XXZ Heisenberg model on a square lattice in the whole range of the XXZ anisotropy by density-matrix renormalization group technique. The validity of our method is confirmed by comparing our results with the previous analytical and numerical studies. Then, as further demonstration, we apply our method to obtain the staggered magnetization for the higher-spin cases from $S=1$ to $S=6$. The accuracy of the obtained results is validated using the series expansion and the spin-wave theory.