玻色BdG系统中布洛赫定理的非微扰失效  

Non-perturbative breakdown of Bloch’s theorem in bosonic BdG systems

作　　者：罗羽轩 杨哲森 Yuxuan Luo;Zhesen Yang(Department of Physics,Xiamen University,Xiamen 361005,China)

机构地区：[1]厦门大学物理科学与技术学院,厦门361005

出　　处：《科学通报》2024年第27期4056-4062,共7页Chinese Science Bulletin

基　　金：国家重点研发计划(2023YFA1407500);国家自然科学基金(12322405,12104450,12047503)资助。

摘　　要：一般而言,厄米系统的开边界条件可视为一种散射势,打破了系统的平移对称性,但仅在微扰意义下使得布洛赫定理失效.这意味,尽管晶格动量不是一个好的量子数,但系统的本征态仍是几个扩展布洛赫波的线性叠加,这与我们对非无序系统的物理直觉是一致的.本文证明布洛赫定理在某些厄米玻色系统中可能是非微扰失效的.系统的准粒子是局域的非布洛赫波的叠加,这些非布洛赫波需要用复动量来刻画,复动量的虚部决定了波的局域性质.为了进一步理解这些准粒子,我们使用了广义布里渊区理论来解释复动量与复能谱的出现,并通过系统的动力学行为展示了布洛赫定理的非微扰失效.本工作是非厄米趋肤效应在厄米系统中的推广,并且揭示了凝聚态物理理论研究的新范式.Bloch's theorem,which is one of the cornerstones of condensed matter physics,has played a fundamental role in the development of many theories,such as the band theory,Fermi liquid theory,and BCS theory.It states that when the system has discrete translational symmetry,the corresponding eigenstate can be labeled by a conserved quantity,or a good quantum number-Crystal momentum.Based on Bloch's theorem,many important physical quantities can be expressed as the integral over the entire Brillouin zone or the Fermi surface.In realistic macroscopic materials,the translational symmetry is explicitly broken down due to the existence of boundaries.It is natural to ask why we can still use Bloch's theorem to understand the physical properties of real materials?In traditional textbooks of solid-state physics,a thermodynamic limit argument is used to explain the above question.Since the lattice size of the macroscopic material is very large,e.g.N=1023,its asymptotic behaviors can be described by the thermodynamic limit N→o.Therefore,if we fix the lattice constant,i.e.,a,the system length will extend to infinity,ie.L=aN-→o.Since wave functions,e.g.y(x)αe**,should be bounded at the infinity,e.g y(x→±o)K o,the corresponding momentum is restricted to be real numbers.This revives Bloch's theorem.Physically,for a finite-size system with open boundary conditions,the boundary only acts the role of scattering potential and can be regarded as a perturbation to the Bloch Hamiltonian.Therefore,the eigenstate of the OBC Hamiltonian is a superposition of all the scattered Bloch waves with the same energy.In this sense,one can say that,although the existence of boundary definitely breaks the translational symmetry,Bloch's theorem is perturbatively broken down,and one can stll use Bloch's theorem to understand the physical properties in real materials.Even for interacting systems,Bloch's theorem is also approximately preserved.Indeed,in a many-body system,the elementary excitations(or quasiparticles)are referred to the eigenmodes wi

关 键 词：趋肤效应 布洛赫定理 广义布里渊区理论 元激发 

分 类 号：O469[理学—凝聚态物理]