Chiral Spin Liquids and Quantum Error Correcting Codes

The possibility of using the two-fold topological degeneracy of spin-1/2 chiral spin liquid states on the torus to construct quantum error correcting codes is investigated. It is shown that codes constructed using these states on finite periodic lattices do not meet the necessary and sufficient conditions for correcting even a single qubit error with perfect fidelity. However, for large enough lattice sizes these conditions are approximately satisfied, and the resulting codes may therefore be viewed as approximate quantum error correcting codes.Comment: 9 pages, 3 figure

Spin and orbital effects in a 2D electron gas in a random magnetic field

Using the method of superbosonization we consider a model of a random magnetic field (RMF) acting on both orbital motion and spin of electrons in two dimensions. The method is based on exact integration over one particle degrees of freedom and reduction of the problem to a functional integral over supermatrices $Q({\bf r},{\bf r^{\prime}})$. We consider a general case when both the direction of the RMF and the g-factor of the Zeeman splitting are arbitrary. Integrating out fast variations of $Q$ we come to a standard collisional unitary non-linear $\sigma$-model. The collision term consists of orbital, spin and effective spin-orbital parts. For a particular problem of a fixed direction of RMF, we show that additional soft excitations identified with spin modes should appear. Considering $\delta$% -correlated weak RMF and putting g=2 we find the transport time $\tau_{tr}$. This time is 2 times smaller than that for spinless particles.Comment: 9 pages, no figure

Magnetoresistance of composite fermions at \nu=1/2

We have studied temperature dependence of both diagonal and Hall resistivity in the vicinity of $\nu=1/2$. Magnetoresistance was found to be positive and almost independent of temperature: temperature enters resistivity as a logarithmic correction. At the same time, no measurable corrections to the Hall resistivity has been found. Neither of these results can be explained within the mean-field theory of composite fermions by an analogy with conventional low-field interaction theory. There is an indication that interactions of composite fermions with fluctuations of the gauge field may reconcile the theory and experiment.Comment: 9 pages, 4 figure

Understanding the dynamics of fractional edge states with composite fermions

Fractional edge states can be viewed as integer edge states of composite fermions. We exploit this to discuss the conductance of the fractional quantized Hall states and the velocity of edge magnetoplasmons.Comment: 3 pages, revte

Quantum duality and Bethe-ansatz for the Hofstadter problem on hexagonal lattice

The Hofstadter problem is studied on hexagonal lattice. We first establish a relation between the spectra for the hexagonal lattice and for its dual he triangular lattice. Following the idea of Faddeev and Kashaev, we then obtain the Bethe-ansatz equations for this system.Comment: 8 pages, latex, revised version for Phys. Lett.

Transport Properties and Density of States of Quantum Wires with Off-diagonal Disorder

We review recent work on the random hopping problem in a quasi-one-dimensional geometry of N coupled chains (quantum wire with off-diagonal disorder). Both density of states and conductance show a remarkable dependence on the parity of N. The theory is compared to numerical simulations.Comment: 8 pages, to appear in Physica E (special issue on Dynamics of Complex Systems); 6 figure

Energy-level statistics and localization of 2d electrons in random magnetic fields

Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this model, extended states have recently been proposed to exist in the middle of the band. In contrast, from our calculations of the large-$s$ behavior of the nearest neighbor level spacing distribution $P(s)$ and from a finite size scaling analysis we find only localized states in the suggested energy and disorder range.Comment: 4 pages LaTeX, 4 eps-figures. to appear in Physica

Electron Localization in a 2D System with Random Magnetic Flux

Using a finite-size scaling method, we calculate the localization properties of a disordered two-dimensional electron system in the presence of a random magnetic field. Below a critical energy $E_c$ all states are localized and the localization length $\xi$ diverges when the Fermi energy approaches the critical energy, {\it i.e.} $\xi(E)\propto |E-E_c|^{-\nu}$. We find that $E_c$ shifts with the strength of the disorder and the amplitude of the random magnetic field while the critical exponent ($\nu\approx 4.8$) remains unchanged indicating universality in this system. Implications on the experiment in half-filling fractional quantum Hall system are also discussed.Comment: 4 pages, RevTex 3.0, 5 figures(PS files available upon request), #phd1

Magnetoresistance of Two-Dimensional Fermions in a Random Magnetic Field

We perform a semiclassical calculation of the magnetoresistance of spinless two-dimensional fermions in a long-range correlated random magnetic field. In the regime relevant for the problem of the half filled Landau level the perturbative Born approximation fails and we develop a new method of solving the Boltzmann equation beyond the relaxation time approximation. In absence of interactions, electron density modulations, in-plane fields, and Fermi surface anisotropy we obtain a quadratic negative magnetoresistance in the weak field limit.Comment: 12 pages, Latex, no figures, Nordita repor

Wavefunction and level statistics of random two dimensional gauge fields

Level and wavefunction statistics have been studied for two dimensional clusters of the square lattice in the presence of random magnetic fluxes. Fluxes traversing lattice plaquettes are distributed uniformly between - (1/2) Phi_0 and (1/2) Phi_0 with Phi_0 the flux quantum. All considered statistics start close to the corresponding Wigner-Dyson distribution for small system sizes and monotonically move towards Poisson statistics as the cluster size increases. Scaling is quite rapid for states close to the band edges but really difficult to observe for states well within the band. Localization properties are discussed considering two different scenarios. Experimental measurement of one of the considered statistics --wavefunction statistics seems the most promising one-- could discern between both possibilities. A real version of the previous model, i.e., a system that is invariant under time reversal, has been studied concurrently to get coincidences and differences with the Hermitian model.Comment: 12 twocolumnn pages in revtex style, 17 postscript figures, to be published in PRB, send comments to [email protected]