Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems

• URL: http://arxiv.org/abs/2307.02993v3
• Date: Fri, 31 May 2024 08:05:49 GMT
• Title: Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems
• Authors: Yecheng Jing, Jian-Jun Dong, Yu-Yu Zhang, Zi-Xiang Hu,
• Abstract summary: We develop a comprehensive framework for studying biorthogonal dynamical quantum phase transitions in non-Hermitian systems. 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.
• Score: 5.50622466592942
• License: http://creativecommons.org/licenses/by/4.0/
• 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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