Fidelity and criticality in the nonreciprocal Aubry-André-Harper model
arxiv(2024)
摘要
We study the critical behaviors of the ground and first excited states in the
one-dimensional nonreciprocal Aubry-André-Harper model using both the
self-normal and biorthogonal fidelity susceptibilities. We demonstrate that
fidelity susceptibilities serve 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, where 𝒫𝒯 transitions occur, the fidelity
susceptibilities exhibit distinct scaling laws, contingent upon whether the
lattice consists of even or odd sites. For even lattices, the self-normal
fidelity susceptibilities near the critical points continue to scale as
N^2. For odd lattices, the biorthogonal fidelity susceptibilities diverge,
while the self-normal fidelity susceptibilities exhibit linear behavior,
indicating a novel scaling law.
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