The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere

Abstract

Defects are common in physical systems with boundaries, impurities or extensive measurements. The interaction between bulk and defect can lead to rich physical phenomena. Defects in gapless phases of matter with conformal symmetry usually flow to a defect conformal field theory (dCFT). Understanding the universal properties of dCFTs is a challenging task. In this paper, we propose a computational strategy applicable to a line defect in arbitrary dimensions. Our main assumption is that the defect has a UV description in terms of a local modification of the Hamiltonian so that we can compute the overlap between low-energy eigenstates of a system with or without the defect insertion. We argue that these overlaps contain a wealth of conformal data, including the $g$-function, which is an RG monotonic quantity that distinguishes different dCFTs, the scaling dimensions of defect creation operators ${\Delta }_{\alpha }^{+0}$ and changing operators ${\Delta }_{\alpha }^{+-}$ that live on the intersection of different types of line defects, and various OPE coefficients. We apply this method to the fuzzy sphere regularization of 3D CFTs and study the magnetic line defect of the 3D Ising CFT. Using exact diagonalization and DMRG, we report the non-perturbative results $g=0.602(2),{\Delta }_0^{+0}=0.108(5)$ and ${\Delta }_0^{+-}=0.84(5)$ for the first time. We also obtain other OPE coefficients and scaling dimensions. Our results have significant physical implications. For example, they constrain the possible occurrence of spontaneous symmetry breaking at line defects of the 3D Ising CFT. Our method can be potentially applied to various other dCFTs, such as plane defects and Wilson lines in gauge theories.

30 pages, 10 figures and 6 tables

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• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model
• A new series of 3D CFTs with $\mathrm{Sp}(N)$ global symmetry on fuzzy sphere
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Conformal Data for the O(3) Wilson-Fisher Conformal Field Theory from Fuzzy Sphere Realization of the Quantum Rotor Model
• Holographic dual of defect CFT with corner contributions
• Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
• Probing Defects with Quantum Simulator Snapshots
• Exploring nontrivial topology at quantum criticality in a superconducting processor
• Deep Boundary Perturbations at a Quantum Critical Point
• A Fuzzy Sphere Journey in Critical Phenomena
• The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere
• Boundary Criticality at the Nishimori Multicritical Point
• From Weyl Anomaly to Defect Supersymmetric Rényi Entropy and Casimir Energy