Long-time dynamics of the infinite-temperature Heisenberg magnet

TL;DR

This paper investigates the long-time dynamics of the infinite-temperature Heisenberg magnet, revealing a classical-quantum correspondence and deriving a specific power-law decay for the local correlator without phenomenological assumptions.

Contribution

It demonstrates that quantum spin correlators at infinite temperature can be computed via classical vector field averages and derives a scaling law for the local correlator.

Findings

Quantum spin correlator equals classical vector field correlator.

Local correlator decays as t^{-6/7} at long times.

Results obtained without phenomenological assumptions.

Abstract

Infinite-temperature long-time dynamics of Heisenberg model ${\bf\hat{H}}=-\frac{1}{2}\sum_{i,j}J_{ij} \hat{\vec{S}}_{i}\hat{\vec{S}}_{j}$ is investigated. It is shown that the quantum spin pair-correlator is equal to the correlator of classically evaluated vector field averaged over the initial conditions with respect to the gaussian measure. In the continious limit case the scaling estimations allow one to find one-point correlator that turns out to be $C(\vec{r}=0;t)\propto const \times t^{-6/7}$. All results are obtained by straightforward procedure without any assumptions of the phenomenological character.