标题： 自由费米子系统中的纠缠负性：重叠矩阵方法 显示英文标题

标题： Entanglement negativity in free-fermion systems: An overlap matrix approach

摘要： 在本文中，我们通过使用重叠矩阵来计算自由费米子系统中的纠缠偏 negativity。 对于三部分系统，如果基态可以分解为模式的三元组，我们证明部分转置的约化密度矩阵可以分解，并且纠缠偏 negativity 具有简单形式。 然而，在三部分系统中，基态的可分解性并不总是成立。 在这种情况下，部分转置的约化密度矩阵可以用矩阵的 Kronecker 积表示。 我们明确计算了 Su-Schrieffer-Heeger 模型、整数量子霍尔态和均匀一维链的纠缠偏 negativity。 我们发现整数量子霍尔态的纠缠偏 negativity 显示出面积定律行为。 对于均匀一维气体中两个相邻区间的纠缠偏 negativity，我们发现与共形场理论一致。 我们的方法提供了一种数值上可行的方法来研究自由费米子系统中的纠缠偏 negativity。 显示英文摘要

摘要： In this paper, we calculate the entanglement negativity in free-fermion systems by use of the overlap matrices. For a tripartite system, if the ground state can be factored into triples of modes, we show that the partially transposed reduced density matrix can be factorized and the entanglement negativity has a simple form. However, the factorability of the ground state in a tripartite system does not hold in general. In this situation, the partially transposed reduced density matrix can be expressed in terms of the Kronecker product of matrices. We explicitly compute the entanglement negativity for the Su-Schrieffer-Heeger model, the integer Quantum Hall state, and a homogeneous one-dimensional chain. We find that the entanglement negativity for the integer quantum Hall states shows an area law behavior. For the entanglement negativity of two adjacent intervals in a homogeneous one-dimensional gas, we find agreement with the conformal field theory. Our method provides a numerically feasible way to study the entanglement negativity in free-fermion systems.