Universal Aspects of High-Temperature Relaxation Dynamics in Random Spin Models

TL;DR

This paper uncovers universal high-temperature spin relaxation behaviors in anisotropic random Heisenberg models with infinite-range interactions, validated by numerical simulations, revealing fundamental insights into quantum many-body dynamics.

Contribution

The study introduces a universal function governing relaxation dynamics in anisotropic Heisenberg models and validates it through numerical methods, extending understanding beyond low-energy regimes.

Findings

Relaxation can be monotonic or oscillatory depending on a universal parameter.

Oscillations occur only when the universal function A>0, with frequency proportional to √A.

The theoretical predictions match numerical simulations even for small system sizes.

Abstract

Universality is a crucial concept in modern physics, allowing us to capture the essential features of a system's behavior using a small set of parameters. In this work, we unveil universal spin relaxation dynamics in anisotropic random Heisenberg models with infinite-range interactions at high temperatures. Starting from a polarized state, the total magnetization can relax monotonically or decay with long-lived oscillations, determined by the sign of a universal single function $A=-\xi_1^2+\xi_2^2-4\xi_2\xi_3+\xi_3^2$. Here $(\xi_1,\xi_3,\xi_3)$ characterizes the anisotropy of the Heisenberg interaction. Furthermore, the oscillation shows up only for $A>0$, with frequency $\Omega \propto \sqrt{A}$. To validate our theory, we compare it to numerical simulations by solving the Kadanoff-Baym (KB) equation with a melon diagram approximation and the exact diagonalization (ED). The results show our theoretical prediction works in both cases, regardless of a small system size $N=8$ in ED simulations. Our study sheds light on the universal aspect of quantum many-body dynamics beyond low energy limit.