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arXiv · 2307.02993

Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems

Yecheng Jing·Jian-Jun Dong·Yu-Yu Zhang·Zi-Xiang Hu
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Abstract

By utilizing biorthogonal bases, we develop a comprehensive framework for studying biorthogonal dynamical quantum phase transitions in non-Hermitian systems. With the help of the previously overlooked associated state, we define the automatically normalized biorthogonal Loschmidt echo. This approach is capable of handling arbitrary non-Hermitian systems with complex eigenvalues and naturally eliminates the negative value of Loschmidt rate obtained without the biorthogonal bases. Taking the non-Hermitian Su-Schrieffer-Heeger model as a concrete example, a $1/2$ change of dynamical topological order parameter in biorthogonal bases is observed which is not shown in self-normal bases. Furthermore, we discover that the periodicity of biorthogonal dynamical quantum phase transitions depends on whether the two-level subsystem at the critical momentum oscillates or reaches a steady state.

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Yecheng Jing, Jian-Jun Dong, Yu-Yu Zhang, Zi-Xiang Hu. 2023-07-06. Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems. https://doi.org/10.1103/physrevlett.132.220402

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