Dynamical Quantum Phase Transitions in a Pseudo-Hermitian Hamiltonian: The Imbalanced-Pairing Kitaev Model

Research Question and Approach

This study investigates the nonequilibrium dynamics of the imbalanced-pairing Kitaev model, a prototypical pseudo-Hermitian system. The researchers examine how a linearly time-dependent chemical potential (a ramp protocol) drives the system across quantum critical points. By employing a biorthogonal framework, they analyze the emergence of dynamical quantum phase transitions (DQPTs), which are characterized by nonanalyticities in the dynamical free-energy density and jumps in a dynamical topological order parameter (DTOP).

The authors demonstrate that DQPTs in this non-Hermitian system are intrinsically linked to the reality of the post-ramp energy spectrum. When the non-Hermiticity parameter is positive, the system behaves similarly to its Hermitian counterpart, exhibiting a single family of critical times when crossing a quantum critical point. However, when the ramp crosses two critical or exceptional points, the behavior changes significantly. The critical sweep velocity required to suppress DQPTs decreases as the non-Hermiticity parameter is reduced, eventually vanishing at the staggered-pairing limit (gamma = -1). Consequently, for values below this limit, DQPTs are entirely absent regardless of the sweep speed.

This work extends the understanding of DQPTs beyond the standard Hermitian paradigm. By applying the biorthogonal framework to a non-Hermitian model without particle-number conservation, the study provides a rigorous method for analyzing nonequilibrium phenomena in dissipative or non-Hermitian quantum systems. These findings are relevant for experimental platforms like photonics, cold atoms, and superconducting circuits, where non-Hermitian dynamics can be engineered to control quantum phase transitions.