论文标题
解析模块化流：免费费米的工具包
Resolving modular flow: a toolkit for free fermions
论文作者
论文摘要
模块化流量是与时空区域相关的可观察到的代数的对称性。与纠缠密切相关，它在信息理论，QFT和重力之间的最新联系中发挥了关键作用。但是，对于高度对称案例以外的作用知之甚少。这项工作的关键思想是在$ 1+1 $尺寸中引入一个新的模块化流动的公式，直接从\ textit {resolvent}工作，这是一种复杂分析中的标准技术。我们为平面，气缸和圆环上的不相交区域介绍了新的结果 - 不是由共形对称性固定的。根据温度和边界条件，这些行为范围从纯粹的局部到非本地的行为，相对于空中分离时的操作员的混合。我们发现模块化的两点函数，其分析结构与控制模块化进化的KMS条件是准确的一致性。我们的现成公式可以提供新的成分，以探索时空与纠缠之间的联系。
Modular flow is a symmetry of the algebra of observables associated to spacetime regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is known about its action beyond highly symmetric cases. The key idea of this work is to introduce a new formula for modular flows for free chiral fermions in $1+1$ dimensions, working directly from the \textit{resolvent}, a standard technique in complex analysis. We present novel results -- not fixed by conformal symmetry -- for disjoint regions on the plane, cylinder and torus. Depending on temperature and boundary conditions, these display different behaviour ranging from purely local to non-local in relation to the mixing of operators at spacelike separation. We find the modular two-point function, whose analytic structure is in precise agreement with the KMS condition that governs modular evolution. Our ready-to-use formulae may provide new ingredients to explore the connection between spacetime and entanglement.
