非互惠奥布里-安德烈-哈珀模型的保真度和临界度

Chen-Chang Zeng, Zhen Cai, Guang-Heng Wang, Gaoyong Sun
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摘要

我们利用自正常和双谐波保真电感研究了一维非互惠的奥布里-安德鲁-哈珀模型中基态和第一激发态的临界行为。我们证明保真度电感可以作为非互惠AAH模型相变的探针。对于以贯穿整个体系的实特征能为特征的基态,临界点附近的两个保真度感生量都以 $N^{2}$ 为标度,这与赫米特 AAH 模型相似。然而,对于发生$\mathcal{PT}$跃迁的第一激发态,保真度易感性表现出不同的缩放规律,这取决于晶格是由偶数位点还是奇数位点组成。对于偶数晶格,临界点附近的自反常保真度感度随着$N^{2}$的增大而增大。对于奇数晶格,双正交保真度电感发散,而自正常保真度电感表现出线性行为,这表明了一种新的缩放规律。
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Fidelity and criticality in the nonreciprocal Aubry-Andr{é}-Harper model
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 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 $\mathcal{PT}$ 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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