A nontrivial bosonic representation of large spin systems at high temperatures

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.