论文标题
终点对激发态模块化汉密尔顿人的贡献
Endpoint contributions to excited-state modular Hamiltonians
论文作者
论文摘要
我们通过用单一操作员扰动真空来计算模块化的汉密尔顿人。我们使用操作员方法并以扰动力的强度进行一阶工作。在大多数情况下，我们将空间分为一半，并专注于通过在空平面上集成本地操作员$ j $而产生的扰动。真空模块化流量下的重量$ n \ geq 2 $的本地操作员为模块化的哈密顿量产生了额外的终点贡献。直观地，这是因为重量$ n \ geq 2 $的运营商可以将自由度从一个地区移动到其补充。端点贡献是无效飞机上$ j $的积分。我们详细介绍了应力张量在两个维度的压力张力扰动，其中可以通过共形转换来验证结果，以及CFT中的标量扰动。这使我们可以猜想适用于分为半空间的任何场理论的端点贡献的一般形式。
We compute modular Hamiltonians for excited states obtained by perturbing the vacuum with a unitary operator. We use operator methods and work to first order in the strength of the perturbation. For the most part we divide space in half and focus on perturbations generated by integrating a local operator $J$ over a null plane. Local operators with weight $n \geq 2$ under vacuum modular flow produce an additional endpoint contribution to the modular Hamiltonian. Intuitively this is because operators with weight $n \geq 2$ can move degrees of freedom from a region to its complement. The endpoint contribution is an integral of $J$ over a null plane. We show this in detail for stress tensor perturbations in two dimensions, where the result can be verified by a conformal transformation, and for scalar perturbations in a CFT. This lets us conjecture a general form for the endpoint contribution that applies to any field theory divided into half-spaces.
