从波函数重叠出发的算子融合：普适有限尺寸修正及其在 Haagerup 模型中的应用
Operator fusion from wavefunction overlaps: Universal finite-size corrections and application to Haagerup model
AI总结：
本文证明临界自旋链的波函数重叠编码中心荷、共形维数与 OPE 系数等全部共形数据及普适有限尺寸修正，并用于确定 Haagerup 模型的中心荷和算子维数。
摘要：
给定一条在长程上由共形场论（CFT）描述的临界量子自旋链，理解其普适共形数据至关重要。其中最重要的组成部分之一是算子乘积展开（OPE）系数，它描述算子之间如何彼此融合。Zou 与 Vidal 在《Phys. Rev. B》105, 125125 中提出，OPE 系数可以通过自旋链低能波函数的重叠来计算。在本工作中，我们证明包括中心荷、共形维数和 OPE 系数在内的所有共形数据都编码在波函数重叠中，并具有依赖于循环 orbifold CFT 算子内容的普适有限尺寸修正。因此，该方法使我们能够仅基于低能本征态数值计算所有共形数据。这些预测在 Ising 模型和 XXZ 模型中得到验证。作为应用，我们研究了近期提出的、由 Haagerup 融合范畴构建的 Haagerup 模型。我们发现其 CFT 的中心荷为 $c \approx 2.1$，且扭曲扇区中最低的自旋-1 算子具有标度维数 $1 < Δ_J \leq 1.4$。
英文摘要：
Given a critical quantum spin chain described by a conformal field theory (CFT) at long distances, it is crucial to understand the universal conformal data. One most important ingredient is the operator product expansion (OPE) coefficients, which describe how operators fuse into each other. It has been proposed in [Zou, Vidal, Phys. Rev. B 105, 125125] that the OPE coefficients can be computed from overlaps of low-energy wavefunctions of the spin chain. In this work, we establish that all conformal data including central charge, conformal dimensions, and OPE coefficients are encoded in the wavefunction overlaps, with universal finite-size corrections that depend on the operator content of the cyclic orbifold CFT. Thus this method allows us to numerically compute all the conformal data based solely on the low-energy eigenstates. The predictions are verified in the Ising and XXZ model. As an application, we study the recently proposed Haagerup model built from the Haagerup fusion category. We find that the CFT has central charge $c \approx 2.1$ and the lowest spin-$1$ operator in the twisted sector has scaling dimension $1 < Δ_J \leq 1.4$.
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