论文标题
在边界存在下，无数迪拉克领域的模块化哈密顿量
Modular Hamiltonians for the massless Dirac field in the presence of a boundary
论文作者
论文摘要
我们研究半线无质量的零dirac fermion间隔的模块化哈密顿人。最一般的边界条件确保了全球能量保护导致考虑两个阶段，其中保留了矢量或轴向对称性。在这两个阶段中，我们以显式形式得出相应的模块化汉密尔顿。它的密度涉及一个本地术语，该术语位于间隔的两个点，一个与另一个偶联。还建立了相关的模块化流。根据相位，它们将磁场与遵循不同模块化轨迹的不同手性或电荷混合。因此，模块化流量保留了矢量或轴向对称性。我们计算沿模块流量的两点相关函数，并表明它们在两个阶段都满足了Kubo-Martin-Schinginger条件。还会得出纠缠熵。
We study the modular Hamiltonians of an interval for the massless Dirac fermion on the half-line. The most general boundary conditions ensuring the global energy conservation lead to consider two phases, where either the vector or the axial symmetry is preserved. In these two phases we derive the corresponding modular Hamiltonian in explicit form. Its density involves a bi-local term localised in two points of the interval, one conjugate to the other. The associated modular flows are also established. Depending on the phase, they mix fields with different chirality or charge that follow different modular trajectories. Accordingly, the modular flow preserves either the vector or the axial symmetry. We compute the two-point correlation functions along the modular flow and show that they satisfy the Kubo-Martin-Schwinger condition in both phases. The entanglement entropies are also derived.
