We report a throughout analysis of the entanglement entropies related to different symmetry sectors in the low-lying primary excited states of a conformal field theory (CFT) with an internal U(1) symmetry. Our findings extend recent results for the ground state. We derive a general expression for the charged moments, i.e. the generalised cumulant generating function, which can be written in terms of correlation functions of the operator that define the state through the CFT operator-state correspondence. We provide explicit analytic computations for the compact boson CFT (aka Luttinger liquid) for the vertex and derivative excitations. The Fourier transform of the charged moments gives the desired symmetry resolved entropies. At the leading order, they satisfy entanglement equipartition, as in the ground state, but we find, within CFT, subleading terms that break it. Our analytical findings are checked against free fermions calculations on a lattice, finding excellent agreement. As a byproduct, we have exact results for the full counting statistics of the U(1) charge in the considered excited states.

中文翻译：

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对称性解决了 CFT 中激发态的纠缠熵

我们报告了对具有内部 U(1) 对称性的共形场理论 (CFT) 的低洼初级激发态中与不同对称扇区相关的纠缠熵的全面分析。我们的发现扩展了基态的最新结果。我们推导出带电矩的一般表达式，即广义累积量生成函数，它可以写成通过 CFT 算子-状态对应定义状态的算子的相关函数。我们为顶点和导数激发的紧凑玻色子 CFT（又名 Luttinger 液体）提供显式解析计算。带电矩的傅立叶变换给出了所需的对称解析熵。在领先阶，它们满足纠缠均分，就像在基态一样，但我们发现，在 CFT 中，打破它的次级术语。我们的分析结果与晶格上的自由费米子计算进行了核对，发现了极好的一致性。作为副产品，我们对所考虑的激发态中 U(1) 电荷的完整计数统计有了准确的结果。