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Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems.

Yecheng Jing1, Jian-Jun Dong1, Yu-Yu Zhang1

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We introduce a new framework for studying dynamical quantum phase transitions in non-Hermitian systems using biorthogonal bases. This method reveals a 1/2 change in the topological order parameter, previously hidden in self-normal bases.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Non-Hermitian systems

Background:

  • Dynamical quantum phase transitions (DQPTs) are crucial for understanding non-Hermitian systems.
  • Standard methods often struggle with complex eigenvalues and negative Loschmidt rates.
  • Biorthogonal bases offer a potential alternative for analyzing these systems.

Purpose of the Study:

  • Develop a comprehensive framework for studying DQPTs in non-Hermitian systems.
  • Introduce an automatically normalized biorthogonal Loschmidt echo.
  • Reveal new phenomena in non-Hermitian DQPTs.

Main Methods:

  • Utilizing biorthogonal bases for theoretical analysis.
  • Defining an automatically normalized biorthogonal Loschmidt echo using associated states.
  • Applying the framework to the non-Hermitian Su-Schrieffer-Heeger model.

Main Results:

  • A comprehensive framework for biorthogonal DQPTs in non-Hermitian systems is established.
  • The associated state enables an automatically normalized biorthogonal Loschmidt echo, handling complex eigenvalues and eliminating negative rates.
  • A 1/2 change in the dynamical topological order parameter is observed in biorthogonal bases, absent in self-normal bases.
  • The periodicity of biorthogonal DQPTs is found to depend on subsystem behavior (oscillation vs. steady state).

Conclusions:

  • The proposed biorthogonal framework provides a robust method for studying DQPTs in non-Hermitian systems.
  • This approach uncovers hidden topological transitions and offers new insights into their periodicity.
  • The findings pave the way for deeper understanding of quantum dynamics in open quantum systems.