论文标题
在缺陷的情况下，模块化的哈密顿量
Modular Hamiltonians for the massless Dirac field in the presence of a defect
论文作者
论文摘要
我们研究了以统一散射矩阵为特征的点状缺陷，在线上的无质量狄拉克场，允许反射和透射。考虑到该系统处于基础状态，我们得出了由两个与缺陷相同距离的距离相同距离的相等间隔给出的子区域的模块化汉密尔顿。在缺陷处缺乏能量耗散意味着存在两个阶段，其中保留了矢量或轴向对称性。除地方术语外，模块化的汉密尔顿人的密度还包含散射依赖的双本地术语的总和，这涉及两个由反射和传播产生的共轭点。 Dirac场的每个组件的模块化流将通过给定初始点的轨迹与通过其反射和透射的共轭点的轨迹混合。我们在这两个阶段沿模块化流的两点相关函数得出了两点相关函数，并表明它们满足了Kubo-Martin-Schinginger条件。还计算纠缠熵，发现它们不取决于散射矩阵。
We study the massless Dirac field on the line in the presence of a point-like defect characterised by a unitary scattering matrix, that allows both reflection and transmission. Considering this system in its ground state, we derive the modular Hamiltonians of the subregion given by the union of two disjoint equal intervals at the same distance from the defect. The absence of energy dissipation at the defect implies the existence of two phases, where either the vector or the axial symmetry is preserved. Besides a local term, the densities of the modular Hamiltonians contain also a sum of scattering dependent bi-local terms, which involve two conjugate points generated by the reflection and the transmission. The modular flows of each component of the Dirac field mix the trajectory passing through a given initial point with the ones passing through its reflected and transmitted conjugate points. We derive the two-point correlation functions along the modular flows in both phases and show that they satisfy the Kubo-Martin-Schwinger condition. The entanglement entropies are also computed, finding that they do not depend on the scattering matrix.
