Valence bond solid order near impurities in two-dimensional quantum antiferromagnets

Abstract

Recent scanning tunnelling microscopy (STM) experiments on underdoped cuprates have displayed modulations in the local electronic density of states which are centered on a Cu-O-Cu bond (Kohsaka et. al., cond-mat/0703309). As a paradigm of the pinning of such bond-centered ordering in strongly correlated systems, we present the theory of valence bond solid (VBS) correlations near a single impurity in a square lattice antiferromagnet. The antiferromagnet is assumed to be in the vicinity of a quantum transition from a magnetically ordered Neel state to a spin-gap state with long-range VBS order. We identify two distinct classes of impurities: i) local modulation in the exchange constants, and ii) a missing or additional spin, for which the impurity perturbation is represented by an uncompensated Berry phase. The `boundary' critical theory for these classes is developed: in the second class we find a `VBS pinwheel' around the impurity, accompanied by a suppression in the VBS susceptibility. Implications for numerical studies of quantum antiferromagnets and for STM experiments on the cuprates are noted.

41 pages, 6 figures; (v2) Minor changes in terminology, added references

References in corpus (36)

• "Deconfined" quantum critical points
• How to detect fluctuating order in the high-temperature superconductors
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• A Four-Unit-Cell Periodic Pattern of Quasiparticle States Surrounding Vortex Cores in Bi2Sr2CaCu2O8+d
• Imaging the Effects of Individual Zinc Impurity Atoms on Superconductivity in Bi2Sr2CaCu2O8+delta
• An Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Local Ordering in the Pseudogap State of the High-T${}_c$ Superconductor Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$
• Vortices with fractional flux in two-gap superconductors and in extended Faddeev model
• Interplay of magnetism and high-Tc superconductivity at individual Ni impurity atoms in Bi2Sr2CaCu2O8+d
• The Theory of Boundary Critical Phenomena
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Quantum Impurity in a Nearly Critical Two Dimensional Antiferromagnet
• Putting competing orders in their place near the Mott transition
• Deconfined quantum criticality and Neel order via dimer disorder
• Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors
• Distinguishing Patterns of Charge Order: Stripes or Checkerboards
• Unidirectional d-wave superconducting domains in the two-dimensional t-J model
• Phase diagram of planar U(1)xU(1) superconductors: condensation of vortices with fractional flux and a superfluid state
• Ordinary, extraordinary, and normal surface transitions: extraordinary-normal equivalence and simple explanation of $|T-T_c{|}^{2-\alpha }$ singularities
• Field- and temperature induced topological phase transitions in the three-dimensional $N$-component London superconductor
• From stripe to checkerboard order on the square lattice in the presence of quenched disorder
• Hole dynamics in an antiferromagnet across a deconfined quantum critical point
• Theory of quantum impurities in spin liquids
• Four-fold structure of vortex core states in Bi2Sr2CaCu2O8 (Bi2212)
• Quantum impurity in an antiferromagnet: non-linear sigma model theory
• The Kondo effect in bosonic spin liquids
• Impurity induced spin texture in quantum critical 2D antiferromagnets
• Critical properties of the N-color London model
• Impurity effects at finite temperature in the two-dimensional S=1/2 Heisenberg antiferromagnet
• $\epsilon$-Expansion of the Conductivity at the Superconductor-Mott Insulator Transition
• Dual vortex theory of doped Mott insulators
• Duality and scaling in 3-dimensional scalar electrodynamics
• Detecting the quantum zero-point motion of vortices in the cuprate superconductors
• Impurity spin textures across conventional and deconfined quantum critical points of two-dimensional antiferromagnets
• Magnetic permeability of near-critical 3d abelian Higgs model and duality

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• Impurity effects in coupled-ladder BiCu2PO6 studied by NMR and quantum Monte Carlo simulations
• Quantum phase transitions beyond the Landau-Ginzburg paradigm and supersymmetry
• Imaging bond order near non-magnetic impurities in square lattice antiferromagnets
• Generalization of the singlet sector valence bond loop algorithm to antiferromagnetic ground states with total spin $S_{tot}=1/2$
• Evidence of a spin liquid phase in the frustrated honeycomb lattice
• Edge and impurity response in two-dimensional quantum antiferromagnets
• Edge effects in the two-dimensional spin-1/2 Heisenberg antiferromagnet
• Overscreened Kondo fixed point in S=1 spin liquid
• Effects of edge disorder in nano-scale antiferromagnetic clusters
• Wilson Loops in Non-Compact U(1) Gauge Theories at Criticality
• Many-body calculation of the spatial extent of the wave-function of a non-magnetic impurity in a d-wave high-temperature superconductor using the t--J model
• Mirror symmetry and the flavor vortex operator in two dimensions