Fidelity and criticality in the nonreciprocal Aubry-Andr{\'e}-Harper model

TL;DR

This paper investigates the phase transition behaviors in the nonreciprocal Aubry-Andr{\'e}-Harper model, revealing how fidelity susceptibilities scale differently for ground and excited states, with unique effects based on lattice parity.

Contribution

It introduces the use of fidelity susceptibilities to probe phase transitions in the nonreciprocal AAH model, highlighting novel scaling laws for excited states and lattice parity effects.

Findings

Fidelity susceptibility scales as N^2 near critical points for ground states.

Excited states show different scaling laws depending on lattice parity.

Biorthogonal fidelity susceptibilities diverge for odd lattices.

Abstract

We study the critical behaviors of the ground and first excited states in the one-dimensional nonreciprocal Aubry-Andr{\'e}-Harper model using both the self-normal and biorthogonal fidelity susceptibilities. We demonstrate that fidelity susceptibility serves as a probe for the phase transition in the nonreciprocal AAH model. For ground states, characterized by real eigenenergies across the entire regime, both fidelity susceptibilities near the critical points scale as $N^{2}$, akin to the Hermitian AAH model. However, for the first-excited states, the fidelity susceptibilities exhibit distinct scaling laws, contingent upon whether the lattice consists of even or odd sites. For even lattices, both the self-normal and biorthogonal fidelity susceptibilities near the critical points continue to scale as $N^{2}$. In contrast, for odd lattices, the biorthogonal fidelity susceptibilities diverge, while the self-normal fidelity susceptibilities exhibit linear behavior, indicating a novel scaling law.