Numerical study of the spin-1/2 Heisenberg antiferromagnet on a 48-site triangular lattice

TL;DR

This study uses a novel Monte Carlo method to analyze the ground state and magnon spectra of the spin-1/2 Heisenberg antiferromagnet on a 48-site triangular lattice, revealing both agreement and differences with spin wave theory.

Contribution

It introduces the stochastic state selection method for studying frustrated quantum spin systems and applies it to a 48-site lattice, providing new insights into the ground state and excitation spectra.

Findings

Sublattice magnetization consistent with linear spin wave theory.

Presence of a Goldstone mode at the ordering wave vector.

Magnon spectra show flat dispersion and downward renormalization.

Abstract

We numerically study the magnetization and the dispersion relation of a frustrated quantum spin system. Our method, which is named the stochastic state selection method, is a kind of Monte Carlo method to give eigenstates of the system through statistical averaging processes. Using the stochastic state selection method with some constraints, we make a successful study of the spin-1/2 Heisenberg antiferromagnet on a 48-site triangular lattice. We calculate the sublattice magnetization and the static structure function in the ground state. Our result on the sublattice magnetization is consistent with the value given by the linear spin wave theory. This adds an evidence for the analysis based on the spontaneous symmetry breaking of the semi-classical Neel order in the ground state. We also evaluate the low-lying one magnon spectra of the model with all wave vectors available on a 48-site triangular lattice. We find that at the ordering wave vector there is a Goldstone mode, which is in good agreement with the result from the spin wave analysis. The magnon spectra with other wave vectors, however, are quite different from results obtained by the linear spin wave theory. We observe a flat dispersion relation with a strong downward renormalization. Our results are compatible with those recently reported in the series expansion study and in the order 1/S calculation of the spin wave analysis.