Quantum Hall Skyrmions with Higher Topological Charge

We have investigated quantum Hall skyrmions at filling factor \nu=1 carrying more than one unit of topological, and hence electric, charge. Using a combination of analytic and numerical methods we find the counterintuitive result that when the Zeeman energy is tuned to values much smaller than the interaction energy (g \mu_B B/(e^2/\epsilon\ell) < 9*10^{-5}),the creation energy of a charge two skyrmion becomes less than twice the creation energy of a charge one skyrmion, i.e. skyrmions bind in pairs. The doubly charged skyrmions are stable to further accretion of charge and exhibit a 10% larger spin per unit charge than charge one skyrmions which would, in principle, signal this pairing.Comment: 4 pages, 3 figures. Submitted to Phys. Rev. B, Rapid Communication

Notes on Infinite Layer Quantum Hall Systems

We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics such as quasiparticles with non-trivial internal structure, irrational braiding phases, and the necessity of a boundary hierarchy construction for interlayer correlated states. The bulk states host a family of surface phases obtained by hybridizing the edge states in each layer. We analyze the surface conduction in these phases by means of sum rule and renormalization group arguments and by explicit computations at weak tunneling in the presence of disorder. We find that in cases where the interlayer electron tunneling is not relevant in the clean limit, the surface phases are chiral semi-metals that conduct only in the presence of disorder or at finite temperature. We show that this class of problems which are naturally formulated as interacting bosonic theories can be fermionized by a general technique that could prove useful in the solution of such ``one and a half'' dimensional problems.Comment: RevTeX, 2 eps figs included, 35p., for a summary see http://xxx.lanl.gov/abs/cond-mat/000643

Evidence for charge-flux duality near the quantum Hall liquid to insulator transition

We examine the longitudinal, non-linear, current-voltage characteristics near the quantum Hall liquid to insulator transition and show that a simple mapping exists between the characteristics on the quantum Hall side and those on the insulating side of the transition. More precisely, at filling factors related by the law of corresponding states the current and voltage simply trade places. We interpret these observations as evidence for the existence, in the composite boson description, of charge-flux duality near disorder dominated transitions in quantum Hall systems. (Appearances notwithstanding, this is an experimental paper.)Comment: 10 pages, Revtex 3.0, 4 uuencoded postscript figure

Analytical theory for proton correlations in common water ice IhI_h

We provide a fully analytical microscopic theory for the proton correlations in water ice $I_h$. We compute the full diffuse elastic neutron scattering structure factor, which we find to be in excellent quantitative agreement with Monte Carlo simulations. It is also in remarkable qualitative agreement with experiment, in the absence of any fitting parameters. Our theory thus provides a tractable analytical starting point to account for more delicate features of the proton correlations in water ice. In addition, it directly determines an effective field theory of water ice as a topological phase.Comment: 5 pages, 3 figure

Nematic Valley Ordering in Quantum Hall Systems

The interplay between quantum Hall ordering and spontaneously broken "internal" symmetries in two-dimensional electron systems with spin or pseudospin degrees of freedom gives rise to a variety of interesting phenomena, including novel phases, phase transitions, and topological excitations. Here we develop a theory of broken-symmetry quantum Hall states, applicable to a class of multi-valley systems, where the symmetry at issue is a point group element that combines a spatial rotation with a permutation of valley indices. The anisotropy of the dispersion relation, generally present in such systems, favors states where all electrons reside in one of the valleys. In a clean system, the valley "pseudo-spin" ordering, or spatial nematic ordering, occurs via a finite temperature transition. In weakly disordered systems, domains of pseudo-spin polarization are formed, which prevents macroscopic valley and nematic ordering; however, the resulting state still asymptotically exhibits the QHE. We discuss the transport properties in the ordered and disordered regimes, and the relation of our results to recent experiments in AlAs.Comment: 6 pages, 2 figure

Nature of the spin liquid state of the Hubbard model on honeycomb lattice

Recent numerical work (Nature 464, 847 (2010)) indicates the existence of a spin liquid phase (SL) that intervenes between the antiferromagnetic and semimetallic phases of the half filled Hubbard model on a honeycomb lattice. To better understand the nature of this exotic phase, we study the quantum $J_1-J_2$ spin model on the honeycomb lattice, which provides an effective description of the Mott insulating region of the Hubbard model. Employing the variational Monte Carlo approach, we analyze the phase diagram of the model, finding a phase transition between antiferromagnet and an unusual $Z_2$ SL state at $J_2/J_1\approx 0.08$, which we identify as the SL phase of the Hubbard model. At higher $J_2/J_1\gtrsim 0.3$ we find a transition to a dimerized state with spontaneously broken rotational symmetry.Comment: 5 pages, 6 figure

Disorder from Disorder in a Strongly Frustrated Transverse Field Ising Chain

We study a one-dimensional chain of corner-sharing triangles with antiferromagnetic Ising interactions along its bonds. Classically, this system is highly frustrated with an extensive entropy at T = 0 and exponentially decaying spin correlations. We show that the introduction of a quantum dynmamics via a transverse magnetic field removes the entropy and opens a gap, but leaves the ground state disordered at all values of the transverse field, thereby providing an analog of the "disorder by disorder" scenario first proposed by Anderson and Fazekas in their search for resonating valence bond states. Our conclusion relies on exact diagonalization calculations as well as on the analysis of a 14th order series expansion about the large transverse field limit. This test suggests that the series method could be used to search for other instances of quantum disordered states in frustrated transverse field magnets in higher dimensions.Comment: 8 pages, RevTex, 7 Figure

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

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