1. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China 2. Key Laboratory of Aerospace Information Materials and Physics(Nanjing University of Aeronautics and Astronautics), MIIT, Nanjing 211106, China 3. Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China
We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.
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