Dynamics of N-spins Quantum Ferromagnet with Uniform Exchange: Exact Solution

TL;DR

This paper provides an exact solution for the dynamics of N-spin quantum ferromagnets with uniform exchange, revealing Gaussian and long-time tail behaviors in autocorrelation functions, and discusses applications in mean-field approximations.

Contribution

It offers the first rigorous calculation of transverse spin autocorrelation functions for arbitrary temperatures in a uniform exchange quantum spin system.

Findings

Autocorrelation functions exhibit Gaussian peaks at small times.

Long-time tails persist in the autocorrelation at large N.

Results suggest a basis for dynamical mean-field approximations.

Abstract

The transverse spin autocorrelation function at an arbitrary temperature are calculated rigorously for the system of $N$ uniformly exchanged quantum spins. At large $N$ the correlator in the para-phase is found to have a Gaussian bump at small times and a non vanishing tail at large times. A possible application of those exact results as forming a starting dynamical mean-field approximation for long-range quantum magnets and an accompanied physical picture are discussed.