Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions

TL;DR

This paper develops a unified geometric framework for understanding dynamical quantum phase transitions in non-Hermitian systems, revealing universal signatures and topological features that extend to open quantum systems.

Contribution

It introduces a comprehensive framework for non-Hermitian DQPTs, including explicit formulas and geometric/topological insights, bridging biorthogonal and non-biorthogonal approaches.

Findings

Universal geometric signature of DQPTs in two-band models

Emergent topological characteristics in non-Hermitian to Hermitian quenches

Fundamental principles linking quantum criticality and topology in open systems

Abstract

We establish a unified framework for dynamical quantum phase transitions (DQPTs) in non-Hermitian systems that encompasses both biorthogonal and self-norm non-biorthogonal formulations for pure and mixed states under quantum quench protocols. Our framework provides explicit expressions for the Loschmidt amplitude, Loschmidt echo, and rate function, revealing a universal geometric signature of DQPTs in the two-band model: orthogonality of two related vectors in two-dimensional real space. Strikingly, we demonstrate that non-biorthogonal quenches from non-Hermitian to Hermitian Hamiltonians under chiral symmetry exhibit emergent topological characteristics of DQPTs, unveiling their fundamental features beyond conventional Hermitian regimes. This work establishes fundamental geometric and topological principles governing quantum criticality in open systems, with implications for quantum sensing and many-body physics in dissipative environments.