Floquet dynamical quantum phase transition in the extended XY model: nonadiabatic to adiabatic topological transition

TL;DR

This paper studies Floquet dynamical quantum phase transitions in an extended XY model, revealing a topological transition from nonadiabatic to adiabatic regimes driven by frequency, with exact calculations of Loschmidt amplitudes and topological invariants.

Contribution

It provides an exact analysis of Floquet DQPTs in the extended XY model, linking topological transitions to adiabaticity and deriving explicit expressions for Loschmidt amplitudes.

Findings

Topological transition from nonadiabatic to adiabatic regimes identified.

Exact expressions for Loschmidt amplitudes derived.

Minimum driving frequency for DQPT determined.

Abstract

We investigate both pure and mixed states Floquet dynamical quantum phase transition (DQPT) in the periodically time-dependent extended XY model. We exactly show that the proposed Floquet Hamiltonian of interacting spins can be expressed as a sum of noninteracting quasi-spins imposed by an effective time dependent magnetic field (Schwinger-Rabi model). The calculated Chern number indicates that there is a topological transition from nonadiabatic to adiabatic regime. In the adiabatic regime, the quasi-spins trace the time dependent effective magnetic field and then oscillate between spin up and down states. While in the nonadiabatic regime, the quasi-spins cannot follow the time dependent effective magnetic field and feel an average magnetic field. We find the range of driving frequency over which the quasi-spins experience adiabatic cyclic processes. Moreover, we obtain the exact expression of the Loschmidt amplitude and generalized Loschmidt amplitude of the proposed Floquet system. The results represent that both pure and mixed states dynamical phase transition occurs when the system evolves adiabatically. In other words, the minimum required driving frequency for the appearance of Floquet DQPT is equal to the threshold frequency needed for transition from nonadiabatic to adiabatic regime.