Abstract
We study theoretically the far-from-equilibrium relaxation dynamics of spin spiral states in the threedimensional 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 the 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 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 nonequilibrium 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)].
Original language | English |
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Article number | 041005 |
Journal | Physical Review X |
Volume | 5 |
Issue number | 4 |
DOIs | |
State | Published - 2015 |
Keywords
- Atomic and molecular physics
- Condensed matter physics
- Nonlinear dynamics