Zheng Zhou, Davide Gaiotto, YinChen He, Yijian Zou
SciPost Phys. 17, 021 (2024) ·
published 25 July 2024

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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 lowenergy 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 $\Delta^{+0}_\alpha$ 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 nonperturbative 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.
SciPost Phys. 15, 072 (2023) ·
published 29 August 2023

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We study the slightly broken higherspin currents in various CFTs with U(1) gauge field, including the tricritical QED, scalar QED, fermionic QED and QEDGrossNeveuYukawa theory. We calculate their anomalous dimension by making use of the classical nonconservation equation and the equations of motion. We find a logarithmic asymptotic behaviour ($\gamma_s\sim 16/(N\pi^2)$ log s ) of the anomalous dimension at large spin $s$, which is different from other interacting CFTs without gauge fields and may indicate certain unique features of gauge theories. We also study slightly broken higherspin currents of the SU(N)$_1$ WZW model at $d=2+\epsilon$ dimensions by formulating them as the QED theory, and we again find its anomalous dimension has a logarithmic asymptotic behaviour with respect to spin. This result resolves the mystery regarding the mechanism of breaking higher spin currents of Virasoro symmetry at $d=2+\epsilon$ dimensions, and may be applicable to other interesting problems such as the $2+\epsilon$ expansion of Ising CFT.
Zheng Zhou (周正), Changle Liu (刘长乐), DongXu Liu (刘东旭), Zheng Yan (严正), Yan Chen (陈焱), XueFeng Zhang (张学锋)
SciPost Phys. 14, 037 (2023) ·
published 16 March 2023

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Incommensurability plays a critical role in many strongly correlated systems. In some cases, the origin of such exotic order can be theoretically understood in the framework of 1d linelike topological excitations known as "quantum strings". Here we study an extended transverse field Ising model on a triangular lattice. Using largescale quantum Monte Carlo simulations, we find that the spatial anisotropy can stabilize an incommensurate phase out of the commensurate clock order. Our results for the structure factor and the string density exhibit a linear relationship between incommensurate ordering wave vector and the density of quantum strings, which is reminiscent of hole density in underdoped cuprate superconductors. When introducing the nextnearestneighbor interaction, we observe a quantum tricritical point out of the incommensurate phase. After carefully analyzing the ground state energies within different string topological sectors, we conclude that this tricriticality is nontrivially caused by effective longrange interstring interactions with two competing terms following different decaying behaviors.
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