Operator fusion from wavefunction overlaps: Universal finite-size corrections and application to Haagerup model

Abstract

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 $1<{\Delta }_J\le 1.4$.

22 pages, 12 figures

References in corpus (9)

• Entanglement negativity in quantum field theory
• Interacting anyons in topological quantum liquids: The golden chain
• Physics at the entangling surface
• Numerical evidence for a Haagerup conformal field theory
• A critical lattice model for a Haagerup conformal field theory
• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
• Multipartitioning topological phases by vertex states and quantum entanglement
• Universal information of critical quantum spin chains from wavefunction overlaps
• Multi-boundary generalization of thermofield double states and their realization in critical quantum spin chains

Cited by in corpus (13)

• Bootstrapping Non-Invertible Symmetries
• Operator Product Expansion Coefficients of the 3D Ising Criticality via Quantum Fuzzy Sphere
• Fermionization of fusion category symmetries in 1+1 dimensions
• The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere
• Finite-size and finite bond dimension effects of tensor network renormalization
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Subfactors and Mathematical Physics
• Multi wavefunction overlap and multi entropy for topological ground states in (2+1) dimensions
• Quantum Cluster State Model with Haagerup Fusion Category Symmetry
• Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
• $G_2$ Integrable Point Characterization via Isotropic Spin-3 Chains
• Tensor network renormalization approach to antiferromagnetic 6-state clock model on the Union Jack lattice
• Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition