Decay of spin-spin correlations in disordered quantum and classical spin chains

TL;DR

This paper investigates how spin-spin correlations decay in disordered one-dimensional spin chains, revealing a strong correspondence between quantum and classical dynamics and showing that disorder effects depend on the spin quantum number.

Contribution

It introduces an effective disorder strength to compare dynamics across different spin quantum numbers and demonstrates quantum-classical correspondence at high temperatures.

Findings

Quantum and classical dynamics agree for small effective disorder.

Disorder effects are stronger for higher spin quantum numbers.

Spectral functions reflect the decay behavior of correlations.

Abstract

The real-time dynamics of equal-site correlation functions is studied for one-dimensional spin models with quenched disorder. Focusing on infinite temperature, we present a comparison between the dynamics of models with different quantum numbers $S = 1/2, 1, 3/2$, as well as of chains consisting of classical spins. Based on this comparison as well as by analyzing the statistics of energy-level spacings, we show that the putative many-body localization transition is shifted to considerably stronger values of disorder for increasing $S$. In this context, we introduce an effective disorder strength $W_\text{eff}$, which provides a mapping between the dynamics for different spin quantum numbers. For small $W_\text{eff}$, we show that the real-time correlations become essentially independent of $S$, and are moreover very well captured by the dynamics of classical spins. Especially for $S = 3/2$, the agreement between quantum and classical dynamics is remarkably observed even for very strong values of disorder. This behavior also reflects itself in the corresponding spectral functions, which are obtained via a Fourier transform from the time to the frequency domain. As an aside, we also comment on the self-averaging properties of the correlation function at weak and strong disorder. Our work sheds light on the correspondence between quantum and classical dynamics at high temperatures and extends our understanding of the dynamics in disordered spin chains beyond the well-studied case of $S=1/2$.