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

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 $A=-\hat{I}{¾}_1^2+\hat{I}{¾}_2^2-4\hat{I}{¾}_2\hat{I}{¾}_3+\hat{I}{¾}_3^2$. Here $(\hat{I}{¾}_1,\hat{I}{¾}_3,\hat{I}{¾}_3)$ characterizes the anisotropy of the Heisenberg interaction. Furthermore, the oscillation shows up only for $A>0$, with frequency $\hat{I}\text{c◯}\propto \sqrt{A}$. 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.

20 pages, 5 figures