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 (40)

• "Deconfined" quantum critical points
• Locally critical quantum phase transitions in strongly correlated metals
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Imaging the Effects of Individual Zinc Impurity Atoms on Superconductivity in Bi2Sr2CaCu2O8+delta
• Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State
• Order and quantum phase transitions in the cuprate superconductors
• On the low energy properies of fermions with singular interactions
• Interplay of magnetism and high-Tc superconductivity at individual Ni impurity atoms in Bi2Sr2CaCu2O8+d
• On the stability of U(1) spin liquids in two dimensions
• Algebraic spin liquid as the mother of many competing orders
• Large N expansion for frustrated and doped quantum antiferromagnets
• Electron spectral function and algebraic spin liquid for the normal state of underdoped high $T_c$ superconductors
• Quantum Impurity in a Nearly Critical Two Dimensional Antiferromagnet
• Spin correlations in the algebraic spin liquid - implications for high Tc superconductors
• Resummation in Hot Field Theories
• Impurities in S=1/2 Heisenberg Antiferromagnetic Chains: Consequences for Neutron Scattering and Knight Shift
• 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 impurity dynamics in two-dimensional antiferromagnets and superconductors
• Universal Magnetic Properties of Frustrated Quantum Antiferromagnets in Two Dimensions
• Critical local moment fluctuations in the Bose-Fermi Kondo model
• Quantum Phase Transition in Frustrated Two-Dimensional Antiferromagnets
• Quantum phase transitions in the Bose-Fermi Kondo model
• Persistence of Li Induced Kondo Moments in the Superconducting State of Cuprates
• 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
• Ordering in Cs2CuCl4: Is there a proximate spin liquid?
• Impurity-induced moments in underdoped cuprates
• Kondo Effect in High-T_c Cuprates
• Local Moment Formation in the Superconducting State of a Doped Mott Insulator
• Order from Disorder: Non Magnetic Impurities in the Spin-gap Phase of the Cuprates
• The Kondo effect in bosonic spin liquids
• Density of States of a d-wave Superconductor in the Presence of Strong Impurity Scatterers: a Non Perturbative Result
• Impurity induced Local Magnetism and Density of States in the superconducting state of YBa2Cu3O7
• Quantum electrodynamics in 2+1 dimensions, confinement, and the stability of U(1) spin liquids
• Static hole in a critical antiferromagnet: field-theoretic renormalization group
• Spin orthogonality catastrophe in two-dimensional antiferromagnets and superconductors
• Impurity effects at finite temperature in the two-dimensional S=1/2 Heisenberg antiferromagnet
• On the spin density wave transition in a two dimensional spin liquid
• On the residual resistivity near a two dimensional metamagnetic quantum critical point

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• Coulomb impurity in graphene
• Strange metals and the AdS/CFT correspondence
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• Critical Spin Liquid versus Valence Bond Glass in Triangular Lattice Organic $\kappa$-(ET)${}_2$Cu${}_2$(CN)${}_3$
• Symmetry Reduction in the Quantum Kagome Antiferromagnet Herbertsmithite
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• Kondo screening in a charge-insulating spinon metal
• Magnetic impurity in a $U(1)$-Spin Liquid with a Spinon Fermi-Surface
• Magnetic Impurity as a Local Probe of the U(1) Quantum Spin Liquid with Spinon Fermi Surface
• $\mu$SR Insight into the Impurity Problem in Quantum Kagome Antiferromagnets
• Studies of non-magnetic impurities in the spin-1/2 Kagome Antiferromagnet
• Dzyaloshinskii-Moriya interactions in valence bond systems
• A Kondo route to spin inhomogeneities in the honeycomb Kitaev model
• Exactly Solvable Topological Chiral Spin Liquid with Random Exchange
• Vacancies in the Kitaev quantum spin liquids on the 3D hyper-honeycomb lattice
• Specific Heat of the Kagome Antiferromagnet Herbertsmithite in High Magnetic Fields
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• Quantum magnets with weakly confined spinons: Multiple length scales and quantum impurities
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• Edge and impurity response in two-dimensional quantum antiferromagnets
• Heat conduction in herbertsmithite: field dependence at the onset of the quantum spin liquid regime
• Impurity spin textures across conventional and deconfined quantum critical points of two-dimensional antiferromagnets
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• $Z_2$ flux binding to higher-spin impurities in the Kitaev spin liquid
• Theory of quasiparticle interference in Kitaev quantum spin liquids
• Effects of impurities in Spin Bose-Metal phase on a two-leg triangular strip
• Overscreened Kondo fixed point in S=1 spin liquid
• Thermal Hall response of an abelian chiral spin liquid at finite temperatures
• Tunneling spectroscopy of the spinon-Kondo effect in one-dimensional Mott insulators
• Wilson Loops in Non-Compact U(1) Gauge Theories at Criticality
• Detecting symmetry fractionalization in gapped quantum spin liquids by magnetic impurities
• Kondo Screening Cloud Scaling: Impurity Entanglement and Magnetization
• Static impurity in a mesoscopic system of SU($N$) fermionic matter-waves
• Boundary quantum criticality in models of magnetic impurities coupled to bosonic baths