Biorthogonal quantum criticality in non-Hermitian many-body systems

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.

Automated summary

The perturbation theory of fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues is developed. The quantum criticality in the non-Hermitian transverse field Ising chain is investigated, revealing a second-order phase transition in the Ising universal class. Numerical computations of critical points and critical exponents from finite-size scaling theory show that the biorthogonal quantum phase transitions are described by biorthogonal fidelity susceptibility instead of conventional fidelity susceptibility.