复相互作用调制的两粒子系统中的局域化转变  

Localization transition in a two-particle system with complex interaction modulation

作　　者：郝佳鑫 徐志浩 HAO Jiaxin;XU Zhihao(State Key Laboratory of Quantum Optics Technologies and Devices,Institute of Theoretical Physics,Shanxi University,Taiyuan 030006,China;Collaborative Innovation Center of Extreme Optics,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学理论物理研究所,光量子技术与器件全国重点实验室,太原030006 [2]山西大学极端光学协同创新中心,太原030006

出　　处：《物理学报》2025年第6期213-219,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12375016,12461160324);山西省基础研究计划(批准号:20210302123442);北京凝聚态物理国家实验室(批准号:2023BNLCMPKF001);山西省“1331工程”重点学科建设计划资助的课题.

摘　　要：研究了一维复相互作用调制的非厄米玻色子模型.通过数值计算能谱的实-复转变、Shannon熵、标准参与比率与拓扑缠绕数发现,当相互作用强度低于临界相互作用强度时,系统的能谱全为实数,处于扩展相,且系统是拓扑平庸的;而当相互作用强度超过临界相互作用强度时,系统开始出现复能谱,处于扩展态与局域态混合相,且此时系统是拓扑非平庸的.计算结果表明,能谱的实-复转变点、扩展-局域的转变点与拓扑转变点相一致.动力学演化结果可以验证系统的实-复转变与局域化转变.最后,提出利用二维光子波导阵列可以模拟这一复相互作用调制的一维玻色子模型.此项工作将为非厄米两体系统的局域性质提供很好的参考.In this work,we investigate a one-dimensional two-boson system with complex interaction modulation,described by the Hamiltonian:H=-JΣ_(j)(c_(j)^(+)c_(j)+1+h.c)+Σ_(j)U/2e^(2iπj)n_(j)(n_(j)-1),where U is the interaction amplitude,and the modulation frequencyα=(√5-1)is an irrational number.The interaction satisfies U_(-j)=U_(j)^(*),which ensures that the system possesses party-time(PT)reversal symmetry.Using the exact diagonalization method,we numerically calculate the real-to-complex transition of the energy spectrum,Shannon entropy,the normalized participation ration,and the topological winding number.For small U,all eigenvalues are real.However,as U increases,eigenvalues corresponding to two particles occupying the same site become complex,marking a PT symmetry-breaking transition at U=2.This point signifies a real-tocomplex transition in the spectrum.To characterize the localization properties of the system,we employ the Shannon entropy and the normalized participation ration(NPR).When U<2,all the eigenstates are extended,exhibiting high Shannon entropy and NPR values.Conversely,for U>2,states with complex eigenvalues show low Shannon entropy and significantly reduced NPR,indicating localization.Meanwhile,states with real eigenvalues remain extended in this regime.We further analyze the topological aspects of the system by using the winding number.A topological phase transition occurs at U=2,where the winding number changes from 0 to 1.This transition coincides with the onset of PT symmetry breaking and the localization transition.The dynamical evolution can be used to detect the localization properties and the real-to-complex transition,with the initial state being two bosons occupying the center site of the chain simultaneously.Finally,we propose an experimental realization by using a two-dimensional linear photonic waveguide array.The modulated interaction can be controlled by adjusting the real part and imaginary part of the refractive index of diagonal waveguide.To simulate this non-Hermitian two-body

关 键 词：非厄米 局域化 拓扑 宇称-时间对称性 

分 类 号：O469[理学—凝聚态物理]