Universal aspects of high-temperature relaxation dynamics in random spin models
Tian-Gang Zhou, Wei Zheng, Pengfei Zhang
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 A = − ξ 1 2 + ξ 2 2 − 4 ξ 2 ξ 3 + ξ 3 2 . Here (\xi_1,\xi_3,\xi_3) ( ξ 1 , ξ 3 , ξ 3 ) characterizes the anisotropy of the Heisenberg interaction. Furthermore, the oscillation shows up only for A>0 A > 0 , with frequency \Omega \propto \sqrt{A} Ω ∝ A . This result is derived from the Kadanoff-Baym equation under the melon diagram approximation, which is consistent with numerical solutions. Furthermore, we verify our theory and approximation using exact diagonalization, albeit for a small system size of N=8 N = 8 . Our study sheds light on the universal aspect of quantum many-body dynamics beyond low energy limit.
arXiv:2305.02359•SciPost Physics•Apr 8, 2025•2 citations