Time reversal symmetry protected chaotic fixed point in the quench dynamics of a topological $p$-wave superfluid

TL;DR

This paper investigates the quench dynamics of a topological p-wave superfluid, revealing a novel chaotic phase protected by time reversal symmetry and mapping out phase boundaries despite nonintegrability.

Contribution

It introduces the phase III' with chaotic oscillations, analyzes stability under symmetry breaking, and connects nonintegrable dynamics to known topological phases.

Findings

Chaotic phase III' emerges from initial fluctuations.

Phase boundaries are exactly mapped in parameter space.

Breaking time reversal symmetry suppresses chaos, leading to topological phases.

Abstract

We study the quench dynamics of a topological $p$-wave superfluid with two competing order parameters, $\Delta_\pm(t)$. When the system is prepared in the $p+ip$ ground state and the interaction strength is quenched, only $\Delta_+(t)$ is nonzero. However, we show that fluctuations in the initial conditions result in the growth of $\Delta_-(t)$ and chaotic oscillations of both order parameters. We term this behavior phase III'. In addition, there are two other types of late time dynamics -- phase I where both order parameters decay to zero and phase II where $\Delta_+(t)$ asymptotes to a nonzero constant while $\Delta_-(t)$ oscillates near zero. Although the model is nonintegrable, we are able to map out the exact phase boundaries in parameter space. Interestingly, we find phase III' is unstable with respect to breaking the time reversal symmetry of the interaction. When one of the order parameters is favored in the Hamiltonian, the other one rapidly vanishes and the previously chaotic phase III' is replaced by the Floquet topological phase III that is seen in the integrable chiral $p$-wave model.