On non-Fermi liquid quantum critical points in heavy fermion metals

Heavy electron metals on the verge of a quantum phase transition to magnetism show a number of unusual non-fermi liquid properties which are poorly understood. This article discusses in a general way various theoretical aspects of this phase transition with an eye toward understanding the non-fermi liquid phenomena. We suggest that the non-Fermi liquid quantum critical state may have a sharp Fermi surface with power law quasiparticles but with a volume not set by the usual Luttinger rule. We also discuss the possibility that the electronic structure change associated with the possible Fermi surface reconstruction may diverge at a different time/length scale from that associated with magnetic phenomena.Comment: 16 pages, 2 figures. Proceedings of workshop on ``Mottness and Quantum Criticality", Tobago, West Indies, June 8-19 (2005), to appear in Annals of Physic

Neel order, quantum spin liquids and quantum criticality in two dimensions

This paper is concerned with the possibility of a direct second order transition out of a collinear Neel phase to a paramagnetic spin liquid in two dimensional quantum antiferromagnets. Contrary to conventional wisdom, we show that such second order quantum transitions can potentially occur to certain spin liquid states popular in theories of the cuprates. We provide a theory of this transition and study its universal properties in an $\epsilon$ expansion. The existence of such a transition has a number of interesting implications for spin liquid based approaches to the underdoped cuprates. In particular it considerably clarifies existing ideas for incorporating antiferromagnetic long range order into such a spin liquid based approach.Comment: 18 pages, 17 figure

Symmetry Protected Topological phases of Quantum Matter

We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting many particle systems, known as Symmetry Protected Topological (SPT) phases. In common with the topological band insulators these states have a bulk gap and no exotic excitations but have non-trivial surface states that are protected by symmetry. We describe the various possible such phases and their properties in three dimensional systems with realistic symmetries. We develop many key ideas of the theory of these states using simple examples. The emphasis is on physical rather than mathematical properties. We survey insights obtained from the study of SPT phases for a number of other theoretical problems.Comment: Invited Review for Annual Reviews of Condensed Matter Physic

Twisted Hubbard Model for Sr2IrO4: Magnetism and Possible High Temperature Superconductivity

Sr2IrO4 has been suggested as a Mott insulator from a single J_eff=1/2 band, similar to the cuprates. However this picture is complicated by the measured large magnetic anisotropy and ferromagnetism. Based on a careful mapping to the J_eff=1/2 (pseudospin-1/2) space, we propose that the low energy electronic structure of Sr2IrO4 can indeed be described by a SU(2) invariant pseudospin-1/2 Hubbard model very similar to that of the cuprates, but with a "twisted" coupling to external magnetic field (a g-tensor with a staggered antisymmetric component). This perspective naturally explains the magnetic properties of Sr2IrO4. We also derive several simple facts based on this mapping and the known results about the Hubbard model and the cuprates, which may be tested in future experiments on Sr2IrO4. In particular we propose that (electron-)doping Sr2IrO4 can potentially realize high-temperature superconductivity.Comment: 5 pages, 1 figure, RevTex4, updated reference

Zero temperature phase transitions in quantum Heisenberg ferromagnets

The purpose of this work is to understand the zero temperature phases, and the phase transitions, of Heisenberg spin systems which can have an extensive, spontaneous magnetic moment; this entails a study of quantum transitions with an order parameter which is also a non-abelian conserved charge. To this end, we introduce and study a new class of lattice models of quantum rotors. We compute their mean-field phase diagrams, and present continuum, quantum field-theoretic descriptions of their low energy properties in different regimes. We argue that, in spatial dimension $d=1$, the phase transitions in itinerant Fermi systems are in the same universality class as the corresponding transitions in certain rotor models. We discuss implications of our results for itinerant fermions systems in higher $d$, and for other physical systems.Comment: 45 pages, REVTEX 3.0, 5 EPS figure

Higher angular momentum Kondo liquids

Conventional heavy Fermi liquid phases of Kondo lattices involve the formation of a "Kondo singlet" between the local moments and the conduction electrons. This Kondo singlet is usually taken to be in an internal s-wave angular momentum state. Here we explore the possibility of phases where the Kondo singlet has internal angular momentum that is d-wave. Such states are readily accessed in a slave boson mean field formulation, and are energetically favorable when the Kondo interaction is between a local moment and an electron at a nearest neighbor site. The properties of the d-wave Kondo liquid are studied. Effective mass and quasiparticle residue show large angle dependence on the Fermi surface. Remarkably in certain cases, the quasiparticle residue goes to zero at isolated points (in two dimensions) on the Fermi surface. The excitations at these points then include a free fractionalized spinon. We also point out the possibility of quantum Hall phenomena in two dimensional Kondo {\em insulators}, if the Kondo singlet has complex internal angular momentum. We suggest that such d-wave Kondo pairing may provide a useful route to thinking about correlated Fermi liquids with strong anisotropy along the Fermi surface.Comment: 12 pages, 7 figure

Topological spin Hall states, charged skyrmions, and superconductivity in two dimensions

We study the properties of two dimensional topological spin hall insulators which arise through spontaneous breakdown of spin symmetry in systems that are spin rotation invariant. Such a phase breaks spin rotation but not time reversal symmetry and has a vector order parameter. Skyrmion configurations in this vector order parameter are shown to have electric charge that is twice the electron charge. When the spin Hall order is destroyed by condensation of skyrmions superconductivity results. This may happen either through doping or at fixed filling by tuning interactions to close the skyrmion gap. In the latter case the superconductor- spin Hall insulator quantum phase transition can be second order even though the two phases break distinct symmetries.Comment: 4 pages, typos corrected, added a footnot

Chiral RKKY interaction in Pr2Ir2O7

Motivated by the potential chiral spin liquid in the metallic spin ice Pr2Ir2O7, we consider how such a chiral state might be selected from the spin ice manifold. We propose that chiral fluctuations of the conducting Ir moments promote ferro-chiral couplings between the local Pr moments, as a chiral analogue of the magnetic RKKY effect. Pr2Ir2O7 provides an ideal setting to explore such a chiral RKKY effect, given the inherent chirality of the spin-ice manifold. We use a slave-rotor calculation on the pyrochlore lattice to estimate the sign and magnitude of the chiral coupling, and find it can easily explain the 1.5K transition to a ferro-chiral state.Comment: 9 pages; 7 figure