Far-from-equilibrium universality in the two-dimensional Heisenberg model

TL;DR

This paper investigates the universal far-from-equilibrium dynamics of the 2D quantum Heisenberg magnet, revealing a long-lived prethermal regime with self-similar spin correlations and identifying a new non-equilibrium universality class.

Contribution

The study analytically derives scaling exponents for the 2D Heisenberg model's non-equilibrium dynamics and demonstrates their universality across various initial conditions, highlighting a new universality class.

Findings

Identification of a long-lived prethermal regime with self-similar correlations

Analytical derivation of spatial-temporal scaling exponents

Distinct scaling behavior due to gapless spin modes protected by SU(2) symmetry

Abstract

We characterize the universal far-from-equilibrium dynamics of the two-dimensional quantum Heisenberg magnet isolated from its environment. For a broad range of initial conditions, we find a long-lived universal prethermal regime characterized by self-similar behavior of spin-spin correlations. We analytically derive the spatial-temporal scaling exponents and find excellent agreement with numerics using phase space methods. The scaling exponents are insensitive to the choice of initial conditions, which include coherent and incoherent spin states with values of total magnetization and energy in a wide range. Compared to previously-studied self-similar dynamics in non-equilibrium $O(n)$ field theories and Bose gases, we find qualitatively distinct scaling behavior originating from the presence of spin modes which remain gapless at long times and which are protected by the global SU(2) symmetry. Our predictions, which suggest a new non-equilibrium universality class, are readily testable in ultra-cold atoms simulators of Heisenberg magnets.