Far-from-equilibrium field theory of many-body quantum spin systems: Prethermalization and relaxation of spin spiral states in three dimensions

TL;DR

This paper develops a field-theoretical approach to study the far-from-equilibrium dynamics of spin spiral states in three-dimensional quantum spin systems, revealing prethermalization, hierarchical relaxation, and fluctuation effects.

Contribution

It introduces a systematic 1/N expansion of a 2PI effective action for spin systems, improving upon mean-field methods for real-time quantum dynamics.

Findings

Discovery of long-lived prethermalized states near phase boundaries

Identification of hierarchical, glassy-like relaxation processes

Prediction of experimentally observable fluctuation-dissipation features

Abstract

We study theoretically the far-from-equilibrium relaxation dynamics of spin spiral states in the three dimensional isotropic Heisenberg model. The investigated problem serves as an archetype for understanding quantum dynamics of isolated many-body systems in the vicinity of a spontaneously broken continuous symmetry. We present a field-theoretical formalism that systematically improves on mean-field for describing the real-time quantum dynamics of generic spin-1/2 systems. This is achieved by mapping spins to Majorana fermions followed by a 1/N expansion of the resulting two-particle irreducible (2PI) effective action. Our analysis reveals rich fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral states. In particular, we find the sudden appearance of long-lived prethermalized plateaus with diverging lifetimes as the spiral winding is tuned toward the thermodynamically stable ferro- or antiferromagnetic phases. The emerging prethermalized states are characterized by different bosonic modes being thermally populated at different effective temperatures, and by a hierarchical relaxation process reminiscent of glassy systems. Spin-spin correlators found by solving the non-equilibrium Bethe-Salpeter equation provide further insight into the dynamic formation of correlations, the fate of unstable collective modes, and the emergence of fluctuation-dissipation relations. Our predictions can be verified experimentally using recent realizations of spin spiral states with ultracold atoms in a quantum gas microscope [S. Hild, et al. Phys. Rev. Lett. 113, 147205 (2014)].