Biorthogonal Dynamical Quantum Phase Transitions in a Non-Hermitian Kitaev Chain

TL;DR

This paper develops a biorthogonal framework to analyze dynamical quantum phase transitions in non-Hermitian topological superconductors, revealing differences from conventional approaches and emphasizing biorthogonality's role.

Contribution

It introduces an associated-state formalism for non-Hermitian systems, reformulates key dynamical quantities, and demonstrates the framework's robustness and importance.

Findings

Critical times differ from conventional self-normal approaches.

The biorthogonal framework is robust for momentum-resolved analysis.

Highlights the essential role of biorthogonality in non-Hermitian dynamics.

Abstract

Dynamical quantum phase transitions in non-Hermitian systems pose fundamental challenges due to the intrinsic biorthogonality of their eigenstates. In this work, we extend a biorthogonal framework to investigate dynamical quantum phase transitions in non-Hermitian topological superconductors. Taking the non-Hermitian Kitaev chain as a prototypical model, we construct an associated-state formalism and reformulate the Loschmidt rate function, dynamical topological order parameter, and dynamical Fisher zeros. Within this framework, we find that the critical times at which dynamical quantum phase transitions occur differ from those based on the conventional self-normal approaches. We further analyze momentum-resolved subsystems at critical momenta and demonstrate the robustness of the biorthogonal framework. Our work highlights the essential role of biorthogonality in nonequilibrium dynamics and establishes a consistent theoretical framework for dynamical quantum phase transitions in non-Hermitian topological superconductors.