Far-from-equilibrium universality in two-dimensional Heisenberg antiferromagnets

TL;DR

This paper investigates the far-from-equilibrium dynamics of two-dimensional Heisenberg antiferromagnets, revealing a universal prethermal regime with self-similar behavior and deriving analytical scaling laws confirmed by numerical simulations.

Contribution

The study introduces an analytical model for the self-similar scaling in 2D Heisenberg antiferromagnets and demonstrates its universality across different initial conditions.

Findings

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

Derivation of spatial-temporal scaling exponents and power-law distributions

Quantitative differences in scaling exponents between antiferromagnetic and ferromagnetic cases

Abstract

We study the far-from-equilibrium dynamics of isolated two-dimensional Heisenberg antiferromagnets. We consider spin spiral initial conditions which imprint a position-dependent staggered-magnetization (or Neel order) in the two-dimensional lattice. Remarkably, we find a long-lived prethermal regime characterized by self-similar behavior of staggered magnetization fluctuations, although the system has no long-range order at finite energy and the staggered magnetization does not couple with conserved charges. Exploiting the separation of length scales introduced by the initial condition, we derive a simplified analytical model that allow us to compute the spatial-temporal scaling exponents and power-law distribution of the staggered magnetization fluctuations analytically, and find excellent agreement with numerical simulations using phase space methods. The scaling exponents are insensitive to details of the initial condition, in particular, no fine-tuning of energy is required to trigger the self-similar scaling regime. Compared with recent results on far-from-equilibrium universality on the Heisenberg ferromagnet, we find quantitatively distinct spatial-temporal scaling exponents, therefore suggesting that the same model with ferromagnetic and antiferromagnetic initial conditions can host different universal regimes. Our predictions are relevant to ultra-cold atoms simulators of Heisenberg magnets and driven antiferromagnetic insulators.