近日，南京航空航天大学的孙高永及其研究团队取得一项新进展。经过不懈努力，他们对扩展硬核玻色子Hatano-Nelson模型中的多体纠缠和能谱团簇进行研究。相关研究成果已于2024年4月10日在国际知名学术期刊《物理评论A》上发表。

该研究团队研究了硬核极限下扩展玻色子Hatano-Nelson模型的多体纠缠和能谱。研究人员证明系统经历了从无能隙相位到电荷密度波相位的相变，并伴随着第一激发态的宇称时间相变。相变的特征是基态双正交序参数的交叉和第一激发态纠缠熵的突变。研究人员通过中心电荷c=1的基态纠缠熵的对数标度验证了无能隙相位。

此外，研究人员还证明了在强近邻相互作用下，所有能谱团簇都会形成椭圆，为此他们建立了一个普遍的标度定律。对于最近邻相互作用，长轴和短轴的长度服从幂律。最后，研究人员推导出了各团簇最外层椭圆环上能级数的精确表达式。

附：英文原文

Title: Many-body entanglement and spectral clusters in the extended hard-core bosonic Hatano-Nelson model

Author: Chao-Ze Lu, Gaoyong Sun

Issue&Volume: 2024/04/10

Abstract: 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 parity-time 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.

DOI: 10.1103/PhysRevA.109.042208

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.042208