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arXiv:cond-mat/0606385 · Physical Review B

Theory of quantum impurities in spin liquids

Alexei K. Kolezhuk, Subir Sachdev A, Rudro R. Biswas, Peiqiu Chen

Published Oct 23, 2006• 61 citations
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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 N\'eel 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 N\'eel-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, organic Mott insulators, and graphene.

DOI
10.1103/physrevb.74.165114

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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)U(1)U(1) spin liquids described by (2+1)(2+1)(2+1)-dimensional conformal field theories (CFT): the staggered flux (sF) spin liquid, and the deconfined critical point between the N'eel 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∕T1∕T1∕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 N'eel-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, organic Mott insulators, and graphene.
We describe the spin distribution in the vicinity of a nonmagnetic impurity in a two-dimensional antiferromagnet undergoing a transition from a magnetically ordered N\'eel state to a paramagnet with a spin gap. The quantum critical ground state in a finite system has total spin S=1∕2S=1∕2S=1∕2 (if the system without the impurity had an even number of S=1∕2S=1∕2S=1∕2 spins), and recent numerical studies in a double layer antiferromagnet [K. H. H\"oglund et al., Phys. Rev. Lett. 98, 087203 (2007)] have shown that the spin has a universal spatial form delocalized across the entire sample. We present the field theory describing the uniform and staggered magnetizations in this spin texture for two classes of antiferromagnets: (i) the transition from a N\'eel state to a paramagnet with local spin singlets, in models with an even number of S=1∕2S=1∕2S=1∕2 spins per unit cell, which are described by a O(3) Landau-Ginzburg-Wilson field theory; and (ii) the transition from a N\'eel state to a valence bond solid, in antiferromagnets with a single S=1∕2S=1∕2S=1∕2 spin per unit cell, which are described by a ``deconfined'' field theory of spinons.
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Many popular models of fractionalized spin liquids contain neutral fermionic spinon excitations on a Fermi surface, carrying unit charges under a compact U(1) gauge force. We argue that except at possible critical points, instanton effects generically render such states unstable to confinement in two spatial dimensions, so that all elementary excitations are gauge neutral, and there is no spinon Fermi surface. Similar results are expected to apply to SU(2) spin liquids. However, fractionalized states can appear when the gauge symmetry is broken down to a discrete subgroup by the Higgs mechanism. Our argument generalizes earlier results on confinement in the pure gauge theory, and arguments for the instability of the U(1) ``staggered flux'' and ``algebraic'' spin liquids with a Dirac spectrum for fermionic spinons.