扩展硬核玻色Hatano-Nelson模型中的多体纠缠与谱簇
Many-body entanglement and spectral clusters in the extended hard-core bosonic Hatano-Nelson model
AI总结：
本研究针对硬核极限下的扩展玻色Hatano-Nelson模型，揭示了伴随$\u200b\mathcal{PT}$相变的无隙-电荷密度波相变特征，验证了无隙相的对数纠缠标度，并建立了强相互作用下能谱椭圆簇的普适标度律与能级数精确表达式。
摘要：
我们研究了硬核极限下扩展玻色Hatano-Nelson模型的多体纠缠与能谱。研究表明，该系统会经历从无隙相到电荷密度波相的相变，同时第一激发态伴随发生$\u200b\mathcal{PT}$相变。该相变的特征为基态双正交序参量的交叉以及第一激发态纠缠熵的突变。无隙相通过基态纠缠熵的对数标度得到验证，其中心电荷$c=1$。此外，我们发现在强最近邻相互作用下，所有能谱簇会形成椭圆结构，并为此建立了普适标度律。结果显示，椭圆的长轴和短轴长度相对于最近邻相互作用服从幂律关系。我们还推导得到了每个谱簇最外层椭圆环上的能级数的精确表达式。
英文摘要：
We study many-body entanglements and spectra of the extended bosonic Hatano-Nelson model in the hard-core limit. We show that the system undergoes a phase transition from a gapless phase to a charge density wave phase accompanied by a $\mathcal{PT}$ transition in the first excited state. The phase transition is characterized by the crossing of the ground-state biorthogonal order parameter and the sudden change of the first excited-state entanglement entropy. The gapless phase is verified by the logarithmic scaling of the ground-state entanglement entropy with the central charge $c=1$. Furthermore, we show that all energy spectral clusters would form ellipses in strong nearest-neighbor interactions, for which we establish a universal scaling law. The lengths of the major and minor axes are shown to obey power laws with respect to the nearest-neighbor interaction. The exact expressions are derived for the numbers of energy levels on the outermost elliptic ring of each clusters.
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