Disordered Kitaev chain with long-range pairing: Loschmidt echo revivals and dynamical phase transitions

TL;DR

This paper investigates the nonequilibrium dynamics and dynamical phase transitions in a long-range Kitaev chain, revealing how long-range pairing affects Loschmidt echo revivals and their robustness against disorder.

Contribution

It demonstrates that long-range pairing modifies revival periodicity and disorder robustness, challenging previous expectations about quantum critical dynamics.

Findings

Revival periodicity breaks for quenches to non-trivial critical points.

Revival periodicity scales inversely with group velocity at trivial critical points for long-range pairing.

Disorder suppresses non-analyticities in the rate function, affecting dynamical phase transitions.

Abstract

We explore the dynamics of long-range Kitaev chain by varying pairing interaction exponent, $\alpha$. It is well known that distinctive characteristics on the nonequilibrium dynamics of a closed quantum system are closely related to the equilibrium phase transitions. Specifically, the return probability of the system to its initial state (Loschmidt echo), in the finite size system, is expected to exhibit very nice periodicity after a sudden quench to a quantum critical point. Where the periodicity of the revivals scales inversely with the maximum of the group velocity. We show that, contrary to expectations, the periodicity of the return probability breaks for a sudden quench to the non-trivial quantum critical point. Further, We find that, the periodicity of return probability scales inversely with the group velocity at the gap closing point for a quench to the trivial critical point of truly long-range pairing case, $\alpha < 1$. In addition, analyzing the effect of averaging quenched disorder shows that the revivals in the short range pairing cases are more robust against disorder than that of the long rang pairing case. We also study the effect of disorder on the non-analyticities of rate function of the return probability which introduced as a witness of the dynamical phase transition. We exhibit that, the non-analyticities in the rate function of return probability are washed out in the presence of strong disorders.