近邻相互作用下mosaic模型的局域化研究  

Localization of Mosaic Model with Neighbor Interaction

作　　者：焦艳 梁军军[1] JIAO Yan;LIANG Junjun(Institute of Theoretical Physics,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学物理电子工程学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2024年第2期385-391,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11875181)。

摘　　要：本文研究了近邻相互作用下一维无自旋费米系统中mosaic模型在非公度光学晶格中的局域化问题,通过调节相互作用强度和准周期势强度来实现热化到多体局域的转变。利用精确对角化方法计算系统中基态与中间六分之一能级对应的本征态的规范参与率,发现在热化相和多体局域相之间存在混合相。在此区域内,系统中间能级对应的激发态比基态更早局域化,这与相互作用Aubry-André模型的混合相性质不同。分别利用密度矩阵重整化群和精确对角化方法,计算基态单粒子激发的密度波动函数和激发态近邻能级间距比与纠缠熵,得到混合相的两条相边界。从相图中可以发现,在多体系统中弱准周期势只能使激发态局域却不能使基态局域,而相互作用的存在降低了基态局域所需的准周期势强度。In this paper,we study the localization problem of mosaic model in a one-dimensional spinless fermi system in an incommensurate optical lattice with near neighbor interactions,which realizes the transition from thermalization to multi-body localization by adjusting the intensity of interaction and quasi-periodic potential.The normalized participation rate of the eigenstates corresponding to the ground state and the middle sixth energy level in the system is calculated by the exact diagonalization method.It is found that there are mixed phases between the thermal phase and the multi-body local phase.In this region,the excited state corresponding to the intermediate energy level of the system is localized earlier than that corresponding to the ground state,which is different from the mixed phase property of the interaction Aubry-Andre model.By means of density matrix renormalization group and exact diagonalization method,the density fluctuation function of ground-state single particle excitation,the ratio of neighbor level spacing and entanglement entropy of excited state are calculated,and two phase boundaries of mixed phase are obtained.It can be seen from the phase diagram that the weak quasi-periodic potential can only localize the excited state but not the ground state in the multi-body system,and the existence of the interaction reduces the required quasi-periodic potential strength for the ground state localization.

关 键 词：多体局域 热化 精确对角化 密度矩阵重整化群 

分 类 号：O413.3[理学—理论物理]