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We study theoretically the far-from-equilibrium relaxation dynamics of spinspiral states in the three dimensional isotropic Heisenberg model. Theinvestigated problem serves as an archetype for understanding quantum dynamicsof isolated many-body systems in the vicinity of a spontaneously brokencontinuous symmetry. We present a field-theoretical formalism thatsystematically improves on mean-field for describing the real-time quantumdynamics of generic spin-1/2 systems. This is achieved by mapping spins toMajorana fermions followed by a 1/N expansion of the resulting two-particleirreducible (2PI) effective action. Our analysis reveals richfluctuation-induced relaxation dynamics in the unitary evolution of spin spiralstates. In particular, we find the sudden appearance of long-livedprethermalized plateaus with diverging lifetimes as the spiral winding is tunedtoward the thermodynamically stable ferro- or antiferromagnetic phases. Theemerging prethermalized states are characterized by different bosonic modesbeing thermally populated at different effective temperatures, and by ahierarchical relaxation process reminiscent of glassy systems. Spin-spincorrelators found by solving the non-equilibrium Bethe-Salpeter equationprovide further insight into the dynamic formation of correlations, the fate ofunstable collective modes, and the emergence of fluctuation-dissipationrelations. Our predictions can be verified experimentally using recentrealizations of spin spiral states with ultracold atoms in a quantum gasmicroscope [S. Hild, et al. Phys. Rev. Lett. 113, 147205 (2014)].

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