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

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 twoparticle 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 ferroor 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 [S. Hild, et al. Phys. Rev. Lett. 113, 147205 (2014)].