论文标题
波力函数重叠的操作员融合：通用有限尺寸校正和对Haagerup模型的应用
Operator fusion from wavefunction overlaps: Universal finite-size corrections and application to Haagerup model
论文作者
论文摘要
鉴于由长距离的保形场理论（CFT）描述的临界量子自旋链，因此了解通用的保形数据至关重要。最重要的成分之一是操作员产品扩展（OPE）系数，该系数描述了操作员如何相互融合。它已在[Zou，vidal，phys。 Rev. B 105，125125]，可以从自旋链的低能波形的重叠中计算OPE系数。在这项工作中，我们确定所有共形数据，包括中央电荷，共形尺寸和OPE系数，都在波函数重叠中编码，其通用有限尺寸的校正取决于环状孔的操作员含量。因此，这种方法使我们能够仅基于低能特征性的数值计算所有共形数据。在ISING和XXZ模型中验证了预测。作为应用程序，我们研究了最近提出的由Haagerup融合类别构建的Haagerup模型。我们发现，CFT具有中央电荷$ C \约2.1 $，最低的旋转$ 1 $ $ 1 $运算符具有缩放尺寸$ 1 <δ_j\ leq 1.4 $。
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 $1 < Δ_J \leq 1.4$.
