Theory of quantum impurities in spin liquids

Abstract

We describe spin correlations in the vicinity of a generalized impurity in a wide class of fractionalized spin liquid states. We argue that the primary characterization of the impurity is its electric charge under the gauge field describing singlet excitations in the spin liquid. We focus on two gapless U(1) spin liquids described by 2+1 dimensional conformal field theories (CFT): the staggered flux (sF) spin liquid, and the deconfined critical point between the Neel and valence-bond-solid (VBS) states. In these cases, the electric charge is argued to be an exactly marginal perturbation of the CFT. Consequently, the impurity susceptibility has a 1/T temperature dependence, with an anomalous Curie constant which is a universal number associated with the CFT. One unexpected feature of the CFT of the sF state is that an applied magnetic field does not induce any staggered spin polarization in the vicinity of the impurity (while such a staggered magnetization is present for the Neel-VBS case). These results differ significantly from earlier theories of vacancies in the sF state, and we explicitly demonstrate how our gauge theory corrects these works. We discuss implications of our results for the cuprate superconductors and organic Mott insulators.

16 pages, 7 figures; (v2) added discussion on relevance to graphene; (v3) corrected estimate of size of bound state in the spin gap phase; (v4) corrected technical problem with pdf; (v5) corrected error in Eq. (2.13), pointed out by Max Metlitski

References in corpus (10)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• On the stability of U(1) spin liquids in two dimensions
• Algebraic spin liquid as the mother of many competing orders
• Phase transitions in the pseudogap Anderson and Kondo models: Critical dimensions, renormalization group, and local-moment criticality
• Emergence of inhomogeneous moments from spin liquid in the triangular-lattice Mott insulator $\kappa$-(ET)${}_2$Cu${}_2$(CN)${}_3$
• Quantum phase transitions in the Bose-Fermi Kondo model
• Upper-critical dimension in a quantum impurity model: Critical theory of the asymmetric pseudogap Kondo problem
• Quantum impurity in an antiferromagnet: non-linear sigma model theory
• Quantum electrodynamics in 2+1 dimensions, confinement, and the stability of U(1) spin liquids

Cited by in corpus (20)

• The electronic properties of graphene
• Properties of an algebraic spin liquid on the kagome lattice
• The Coulomb impurity problem in graphene
• Spin-orbit effects in Na${}_4$Ir${}_3$O${}_8$, a hyper-kagomé lattice antiferromagnet
• Density-Functional Theory of Graphene Sheets
• Screening of Coulomb Impurities in Graphene
• Coulomb impurity in graphene
• Strange metals and the AdS/CFT correspondence
• Hole dynamics in an antiferromagnet across a deconfined quantum critical point
• Symmetry Reduction in the Quantum Kagome Antiferromagnet Herbertsmithite
• Nature of the spin liquid ground state in a breathing kagome compound studied by NMR and series expansion
• Spectral function of a localized fermion coupled to the Wilson-Fisher conformal field theory
• Valence bond solid order near impurities in two-dimensional quantum antiferromagnets
• Studies of non-magnetic impurities in the spin-1/2 Kagome Antiferromagnet
• Dzyaloshinskii-Moriya interactions in valence bond systems
• Quantum magnets with weakly confined spinons: Multiple length scales and quantum impurities
• Edge and impurity response in two-dimensional quantum antiferromagnets
• Impurity spin textures across conventional and deconfined quantum critical points of two-dimensional antiferromagnets
• Wilson Loops in Non-Compact U(1) Gauge Theories at Criticality
• Boundary quantum criticality in models of magnetic impurities coupled to bosonic baths