发表机构
School of Quantum, University of Chinese Academy of Sciences（中国科学院大学量子学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于扭结算符关联函数的普适实空间公式，用于从二维有能隙量子系统中提取手性中心荷，并在场论和晶格模型中验证，为手性拓扑相的表征提供了系统框架。
AI 中文摘要
近年来，基于纠缠的量子物质相表征取得了显著进展，由于其实验和理论上的相关性，实空间公式引起了越来越多的关注。对于二维有能隙的量子系统，我们提出了一个基于扭结算符关联函数 $Z_{g,h}=\langle\psi^{(N)}\rvert\mathcal{T}_A(g)\mathcal{T}_B(h)\mathcal{T}_C(g)\mathcal{T}_C(h)\lvert\psi^{(N)}\rangle$ 的手性中心荷的普适实空间公式，其中 $\lvert\psi^{(N)}\rangle=\lvert\psi\rangle^{\otimes N}$ 是 $N$ 拷贝态，$g,h\in S_N$ 是置换。扭结算符 $\mathcal{T}_R(g)$ 根据 $g$ 对区域 $R$ 内的 $N$ 个副本进行置换。对于满足球面条件的对 $(g,h)$，我们证明关联函数的相位由手性中心荷 $\mathfrak{c}_{-}$ 通过 $Z_{g,h}/\left\lvert Z_{g,h}\right\rvert=(\theta_g\theta_h/\theta_{gh})^{\mathfrak{c}_{-}}$ 决定，其中 $\theta_g^{\mathfrak{c}_{-}}$ 是由 $g\in S_N$ 标记的扭结缺陷的拓扑自旋。该构造适用于玻色子和费米子系统。我们在适当的假设下在场论框架内推导了该公式，并在微观晶格模型中进行了数值测试。我们的结果建立了实空间纠缠结构与手性中心荷之间的普适联系，为直接在晶格上表征手性拓扑相提供了系统框架。
英文摘要
Recent years have witnessed substantial progress in the entanglement-based characterization of quantum phases of matter, with growing interest in real-space formulas due to their theoretical and experimental relevance. For two-dimensional gapped quantum systems, we propose a universal real-space formula for the chiral central charge based on the twist-operator correlator $Z_{g,h}=\langleψ^{(N)}\rvert\mathcal{T}_A(g)\mathcal{T}_B(h)\mathcal{T}_C(g)\mathcal{T}_C(h)\lvertψ^{(N)}\rangle$, where $\lvertψ^{(N)}\rangle=\lvertψ\rangle^{\otimes N}$ is the $N$-copy state and $g,h\in S_N$ are permutations. The twist operator $\mathcal{T}_R(g)$ permutes the $N$ replicas within region $R$ according to $g$. For pairs $(g,h)$ satisfying the spherical condition, we show that the phase of the correlator is determined by the chiral central charge $\mathfrak{c}_{-}$ through $Z_{g,h}/\left\lvert Z_{g,h}\right\rvert=(θ_gθ_h/θ_{gh})^{\mathfrak{c}_{-}}$, where $θ_g^{\mathfrak{c}_{-}}$ is the topological spin of the twist defect labeled by $g\in S_N$. The construction applies to both bosonic and fermionic systems. We derive the formula within a field-theoretic framework under suitable assumptions and further test it numerically in microscopic lattice models. Our results establish a universal connection between real-space entanglement structures and the chiral central charge, providing a systematic framework for characterizing chiral topological phases directly on the lattice.
CommentsMain text with SupplementalMaterial
