Magnetic impurities at quantum critical points: large-$N$ expansion and SPT connections

Abstract

In symmetry protected topological (SPT) phases, the combination of symmetries and a bulk gap stabilizes protected modes at surfaces or at topological defects. Understanding the fate of these modes at a quantum critical point, when the protecting symmetries are on the verge of being broken, is an outstanding problem. This interplay of topology and criticality must incorporate both the bulk dynamics of critical points, often described by nontrivial conformal field theories, and SPT physics. Here, we study the simplest nontrivial setting - that of a 0+1 dimensional topological mode - a quantum spin - coupled to a 2+1D critical bulk. Using the large-$N$ technique we solve a series of models which, as a consequence of topology, demonstrate intermediate coupling fixed points. We compare our results to previous numerical simulations and find good agreement. We also point out intriguing connections to generalized Kondo problems and Sachdev-Ye-Kitaev (SYK) models. In particular, we show that a Luttinger theorem derived for the complex SYK models, that relates the charge density to particle-hole asymmetry, also holds in our setting. These results should help stimulate further analytical study of the interplay between SPT physics and quantum criticality.

Published version. Only minor modifications compared to v1. Main text 19 pages, 8 figures

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• Pivot Hamiltonians as generators of symmetry and entanglement
• Universal entanglement spectrum in gapless symmetry protected topological states
• Analytic bootstrap for the localized magnetic field
• Wilson loop in general representation and RG flow in 1d defect QFT
• The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere
• Phases of Wilson Lines in Conformal Field Theories
• Edge physics at the deconfined transition between a quantum spin Hall insulator and a superconductor
• Building models of topological quantum criticality from pivot Hamiltonians
• RG flows on two-dimensional spherical defects
• Solving Conformal Defects in 3D Conformal Field Theory using Fuzzy Sphere Regularization
• Analytic bootstrap for magnetic impurities
• Quantum extraordinary-log universality of boundary critical behavior
• Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge
• Boundary and defect criticality in topological insulators and superconductors
• Deconfined Quantum Critical Point with Non-locality