Universal Aspects of High-Temperature Relaxation Dynamics in Random Spin Models
arXiv:2305.02359 · doi:10.21468/SciPostPhys.18.4.120
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 . Here characterizes the anisotropy of the Heisenberg interaction. Furthermore, the oscillation shows up only for , with frequency . 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 in ED simulations. Our study sheds light on the universal aspect of quantum many-body dynamics beyond low energy limit.
20 pages, 5 figures
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