标题： 一维超导体中的涌现边界超对称性 显示英文标题

标题： Emergent boundary supersymmetry in a one dimensional superconductor

摘要： 一维量子系统中体性质与边界条件之间的相互作用，引发了许多有趣的物理现象。 其中包括零能模式的出现，这些零能模式对许多领域都具有重要意义。 在这项工作中，我们研究了当边界条件是动态的且由与某些量子自由度耦合引起的零能模式的存在情况。 具体而言，我们研究了一维单态超导体，该模型由Gross-Neveu场论描述，并通过自旋交换相互作用与其边界处的自旋 $\frac{1}{2}$ 磁性杂质耦合。 我们使用嵌套坐标Bethe假设方法精确求解了任意体耦合强度和杂质耦合强度的情况，并证明该系统表现出丰富的边界相结构。 对于一定的耦合范围，低能自由度形成超对称 $spl(2,1)\otimes spl(2,1)$ 代数的不可约表示，在特定点上这些表示变得退化，表明低能边界自由度中存在超对称性。 我们证明在超对称点上存在将一个基态映射到另一个基态的精确零能模式。 我们将这些模式用代数生成元来表达。 显示英文摘要

摘要： The interplay between bulk properties and boundary conditions in one-dimensional quantum systems, gives rise to many intriguing phenomena. These include the emergence of zero energy modes which are of significant interest to a variety of fields. In this work we investigate the presence of such zero modes in cases where the boundary conditions are dynamical and arise due to the coupling to some quantum degrees of freedom. In particular, we study a one-dimensional spin-singlet superconductor, modeled by the Gross-Neveu field theory, coupled to spin $\frac{1}{2}$ magnetic impurities at its boundaries via a spin-exchange interaction. We solve the model exactly for arbitrary values of the bulk and the impurity coupling strengths using nested coordinate Bethe ansatz and show that the system exhibits a rich boundary phase structure. For a range of couplings, the low energy degrees of freedom form irreducible representations of the supersymmetric $spl(2,1)\otimes spl(2,1)$ algebra which become degenerate at a specific point, indicating the emergence of supersymmetry in the low energy boundary degrees of freedom. We show that at the supersymmetric point there exist exact zero energy modes that map one ground state with the other. We express these in terms of the generators of the algebra.