Quantum dynamics of a spin model with an extensive degeneracy

TL;DR

This paper investigates how extensive degeneracy influences quantum dynamics in a one-dimensional spin model, revealing deviations from standard behavior, suppression of oscillations, and emergent symmetries under periodic driving.

Contribution

It uncovers the effects of extensive degeneracy on quantum dynamics, including non-Kibble-Zurek behavior, suppressed St"uckelberg oscillations, and emergent $U(1)$ symmetry at specific drive frequencies.

Findings

Deviation from Kibble-Zurek scaling during ramp through degeneracy

Suppression of St"uckelberg oscillations in double passage scenarios

Emergent $U(1)$ symmetry at certain drive frequencies

Abstract

We study the role played by extensive degeneracy in shaping the nature of the quantum dynamics of a one-dimensional spin model for both ramp and periodic drive protocols. The model displays an extensive degenerate manifold of states for a specific value of one of the parameters of its Hamiltonian. We study a linear ramp which takes the spin model through this degenerate point and show that it leads to a deviation from the usual Kibble-Zurek behavior. We also study the St\"uckelberg oscillations in such a model for a ramp which passes twice through the degenerate point. Our study indicates that such oscillations are strongly suppressed leading to a distinct behavior compared to those arising from double passage through a quantum critical point. Finally, we study the periodic dynamics of the model and show, for a large drive amplitude, the existence of special drive frequencies at which the system exhibits an approximate emergent $U(1)$ symmetry. We study the effect of this emergent symmetry on the correlators of the driven system and demonstrate the existence of dynamic symmetry restoration at these frequencies. We study the fate of the emergent symmetry when the drive amplitude is decreased and discuss possible experiments to test our theory.