Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model

TL;DR

This paper investigates dynamical quantum phase transitions in the two-dimensional Kitaev honeycomb model, revealing how quenches across phase boundaries induce non-analytic behaviors in the Loschmidt echo, with results extending to higher dimensions.

Contribution

It demonstrates the occurrence of DQPTs in the Kitaev honeycomb model and relates these transitions to the model's dimensionality and phase boundary quenches.

Findings

DQPTs occur after quenches across phase boundaries or within the massless phase.

Discontinuities in the Loschmidt echo's derivatives are linked to the system's dimensionality.

Long-time stationary values of the rate function correlate with DQPTs.

Abstract

The notion of a dynamical quantum phase transition (DQPT) was recently introduced in [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)] as the non-analytic behavior of the Loschmidt echo at critical times in the thermodynamic limit. In this work the quench dynamics in the ground state sector of the two-dimensional Kitaev honeycomb model are studied regarding the occurrence of DQPTs. For general two-dimensional systems of BCS-type it is demonstrated how the zeros of the Loschmidt echo coalesce to areas in the thermodynamic limit, implying that DQPTs occur as discontinuities in the second derivative. In the Kitaev honeycomb model DQPTs appear after quenches across a phase boundary or within the massless phase. In the 1d limit of the Kitaev honeycomb model it becomes clear that the discontinuity in the higher derivative is intimately related to the higher dimensionality of the non-degenerate model. Moreover, there is a strong connection between the stationary value of the rate function of the Loschmidt echo after long times and the occurrence of DQPTs in this model.