A nontrivial bosonic representation of large spin systems at high temperatures

TL;DR

This paper introduces a bosonization scheme for large spin systems at high temperatures, showing that collective spin operators behave like harmonic oscillators in thermal equilibrium, with applications to the XY model.

Contribution

It presents a novel bosonic representation of large spin operators at high temperature, linking them to harmonic oscillators in thermal states, which is a new approach in spin system analysis.

Findings

Spin operators behave like harmonic oscillators at large N and high T.

The z component corresponds to a ground-state harmonic oscillator.

Application to the XY Hamiltonian demonstrates the scheme's utility.

Abstract

We report on a nontrivial bosonization scheme for spin operators. It is shown that in the large $N$ limit, at infinite temperature, the operators $\sum_{k=1}^N \hat s_{k\pm}/\sqrt{N}$ behave like the creation and annihilation operators, $a^\dag$ and $a$, corresponding to a harmonic oscillator in thermal equilibrium, whose temperature and frequency are related by $\hbar\omega/k_B T=\ln 3$. The $z$ component is found to be equivalent to the position variable of another harmonic oscillator occupying its ground Gaussian state at zero temperature. The obtained results are applied to the Heisenberg XY Hamiltonian at finite temperature.