Fidelity and criticality in the nonreciprocal Aubry-Andr{é}-Harper model

Abstract

We study the critical behaviors of the ground and first excited states in the one-dimensional nonreciprocal Aubry-Andr{é}-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.

6 pages, 5 figures

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Cited by in corpus (2)

• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials