Dynamics of a quantum phase transition in the Aubry-Andr\'{e}-Harper model with $p$-wave superconductivity

TL;DR

This paper explores the nonequilibrium dynamics of a one-dimensional Aubry-André-Harper model with p-wave superconductivity, revealing unique critical exponents and quench behaviors across different phases.

Contribution

It provides the first analysis of slow and sudden quench dynamics in this model, identifying distinct critical exponents and phase transition behaviors.

Findings

Kibble-Zurek scaling in slow quenches with specific critical exponents

Loschmidt echo vanishes when initial and final phases differ

Critical phase exhibits unique dynamical behaviors during quenches

Abstract

We investigate the nonequilibrium dynamics of the one-dimension Aubry-Andr\'{e}-Harper model with $p$-wave superconductivity by changing the potential strength with slow and sudden quench. Firstly, we study the slow quench dynamics from localized phase to critical phase by linearly decreasing the potential strength $V$. The localization length is finite and its scaling obeys the Kibble-Zurek mechanism. The results show that the second-order phase transition line shares the same critical exponent $z\nu$, giving the correlation length $\nu=0.997$ and dynamical exponent $z=1.373$, which are different from the Aubry-Andr\'{e} model. Secondly, we also study the sudden quench dynamics between three different phases: localized phase, critical phase, and extended phase. In the limit of $V=0$ and $V=\infty$, we analytically study the sudden quench dynamics via the Loschmidt echo. The results suggest that, if the initial state and the post-quench Hamiltonian are in different phases, the Loschmidt echo vanishes at some time intervals. Furthermore, we found that, if the initial value is in the critical phase, the direction of the quench is the same as one of the two limits mentioned before, and similar behaviors will occur.