Biorthogonal quantum criticality in non-Hermitian many-body systems

TL;DR

This paper develops a perturbation theory for fidelity susceptibility in non-Hermitian many-body systems and reveals a second-order quantum phase transition characterized by biorthogonal fidelity susceptibility.

Contribution

It introduces a novel perturbation approach for biorthogonal bases and demonstrates that biorthogonal fidelity susceptibility captures quantum criticality in non-Hermitian systems.

Findings

Identifies a second-order phase transition in the non-Hermitian transverse field Ising chain.

Shows that biorthogonal fidelity susceptibility effectively describes quantum phase transitions.

Provides numerical evidence for critical points and exponents using finite-size scaling.

Abstract

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 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.