Skyrmions in Higher Landau Levels

We calculate the energies of quasiparticles with large numbers of reversed spins (``skyrmions'') for odd integer filling factors 2k+1, k is greater than or equals 1. We find, in contrast with the known result for filling factor equals 1 (k = 0), that these quasiparticles always have higher energy than the fully polarized ones and hence are not the low energy charged excitations, even at small Zeeman energies. It follows that skyrmions are the relevant quasiparticles only at filling factors 1, 1/3 and 1/5.Comment: 10 pages, RevTe

Liquid-gas and other unusual thermal phase transitions in some large-N magnets

Much insight into the low temperature properties of quantum magnets has been gained by generalizing them to symmetry groups of order N, and then studying the large N limit. In this paper we consider an unusual aspect of their finite temperature behavior--their exhibiting a phase transition between a perfectly paramagetic state and a paramagnetic state with a finite correlation length at N = \infty. We analyze this phenomenon in some detail in the large ``spin'' (classical) limit of the SU(N) ferromagnet which is also a lattice discretization of the CP^{N-1} model. We show that at N = \infty the order of the transition is governed by lattice connectivity. At finite values of N, the transition goes away in one or less dimension but survives on many lattices in two dimensions and higher, for sufficiently large N. The latter conclusion contradicts a recent conjecture of Sokal and Starinets, yet is consistent with the known finite temperature behavior of the SU(2) case. We also report closely related first order paramagnet-ferromagnet transitions at large N and shed light on a violation of Elitzur's theorem at infinite N via the large q limit of the q-state Potts model, reformulated as an Ising gauge theory.Comment: 27 pages, 7 figures. Added clarifications requested by a refere

A New Transport Regime in the Quantum Hall Effect

This paper describes an experimental identification and characterization of a new low temperature transport regime near the quantum Hall-to-insulator transition. In this regime, a wide range of transport data are compactly described by a simple phenomenological form which, on the one hand, is inconsistent with either quantum Hall or insulating behavior and, on the other hand, is also clearly at odds with a quantum-critical, or scaling, description. We are unable to determine whether this new regime represents a clearly defined state or is a consequence of finite temperature and sample-size measurements.Comment: Revtex, 3 pages, 2 figure

Statistics of skyrmions in Quantum Hall systems

We analyze statistical interactions of skyrmions in the quantum Hall system near a critical filling fraction in the framework of the Ginzburg-Landau model. The phase picked up by the wave-function during an exchange of two skyrmions close to $\nu=1/(2n+1)$ is $\pi[S+1/2(2n+1)]$, where $S$ is the skyrmion's spin. In the same setting an exchange of two fully polarized vortices gives rise to the phase $\pi/(2n+1)$. Skyrmions with odd and even numbers of reversed spins have different quantum statistics. Condensation of skyrmions with an even number of reversed spins leads to filling fractions with odd denominators, while condensation of those with an odd number of reversed spins gives rise to filling fractions with even denominators.Comment: 6 pages in Latex. addendum - skyrmions with odd or even number of reversed spins have different quantum statistics. They condense to form respectively even or odd denominator filling fraction state

Fractional Spin for Quantum Hall Effect Quasiparticles

We investigate the issue of whether quasiparticles in the fractional quantum Hall effect possess a fractional intrinsic spin. The presence of such a spin $S$ is suggested by the spin-statistics relation $S=\theta/2\pi$, with $\theta$ being the statistical angle, and, on a sphere, is required for consistent quantization of one or more quasiparticles. By performing Berry-phase calculations for quasiparticles on a sphere we find that there are two terms, of different origin, that couple to the curvature and can be interpreted as parts of the quasiparticle spin. One, due to self-interaction, has the same value for both the quasihole and quasielectron, and fulfills the spin-statistics relation. The other is a kinematical effect and has opposite signs for the quasihole and quasielectron. The total spin thus agrees with a generalized spin-statistics theorem $(S_{qh} + S_{qe})/2 = \theta/2\pi$. On the plane, we do not find any corresponding terms.Comment: 15 pages, RevTeX-3.

Flux Hamiltonians, Lie Algebras and Root Lattices With Minuscule Decorations

We study a family of Hamiltonians of fermions hopping on a set of lattices in the presence of a background gauge field. The lattices are constructed by decorating the root lattices of various Lie algebras with their minuscule representations. The Hamiltonians are, in momentum space, themselves elements of the Lie algebras in these same representations. We describe various interesting aspects of the spectra--which exhibit a family resemblance to the Dirac spectrum, and in many cases are able to relate them to known facts about the relevant Lie algebras. Interestingly, various realizable lattices such as the kagom\'{e} and pyrochlore can be given this Lie algebraic interpretation and the particular flux Hamiltonians arise as mean-field Hamiltonians for spin-1/2 Heisenberg models on these lattices

Stripes in Quantum Hall Double Layer Systems

We present results of a study of double layer quantum Hall systems in which each layer has a high-index Landau level that is half-filled. Hartree-Fock calculations indicate that, above a critical layer separation, the system becomes unstable to the formation of a unidirectional coherent charge density wave (UCCDW), which is related to stripe states in single layer systems. The UCCDW state supports a quantized Hall effect when there is tunneling between layers, and is {\it always} stable against formation of an isotropic Wigner crystal for Landau indices $N \ge 1$. The state does become unstable to the formation of modulations within the stripes at large enough layer separation. The UCCDW state supports low-energy modes associated with interlayer coherence. The coherence allows the formation of charged soliton excitations, which become gapless in the limit of vanishing tunneling. We argue that this may result in a novel {\it ``critical Hall state''}, characterized by a power law $I-V$ in tunneling experiments.Comment: 10 pages, 8 figures include

Dynamics of the Compact, Ferromagnetic \nu=1 Edge

We consider the edge dynamics of a compact, fully spin polarized state at filling factor $\nu=1$. We show that there are two sets of collective excitations localized near the edge: the much studied, gapless, edge magnetoplasmon but also an additional edge spin wave that splits off below the bulk spin wave continuum. We show that both of these excitations can soften at finite wave-vectors as the potential confining the system is softened, thereby leading to edge reconstruction by spin texture or charge density wave formation. We note that a commonly employed model of the edge confining potential is non-generic in that it systematically underestimates the texturing instability.Comment: 13 pages, 7 figures, Revte

Hall Conductivity near the z=2 Superconductor-Insulator Transition in 2D

We analyze here the behavior of the Hall conductivity $\sigma_{xy}$ near a $z=2$ insulator-superconductor quantum critical point in a perpendicular magnetic field. We show that the form of the conductivity is sensitive to the presence of dissipation $\eta$, and depends non-monotonically on $H$ once $\eta$ is weak enough. $\sigma_{xy}$ passes through a maximum at $H \sim \eta T$ in the quantum critical regime, suggesting that the limits $H \to 0$ and $\eta \to 0$ do not commute.Comment: 4 pages, 1 .eps figure, to appear in Phys. Rev.

Feynman's Propagator Applied to Network Models of Localization

Network models of dirty electronic systems are mapped onto an interacting field theory of lower dimensionality by intepreting one space dimension as time. This is accomplished via Feynman's interpretation of anti-particles as particles moving backwards in time. The method developed maps calculation of the moments of the Landauer conductance onto calculation of correlation functions of an interacting field theory of bosons and fermions. The resulting field theories are supersymmetric and closely related to the supersymmetric spin-chain representations of network models recently discussed by various authors. As an application of the method, the two-edge Chalker-Coddington model is shown to be Anderson localized, and a delocalization transition in a related two-edge network model (recently discussed by Balents and Fisher) is studied by calculation of the average Landauer conductance.Comment: Latex, 14 pages, 2 fig