Christopher Mudry

Fractional Quantum Hall States at Zero Magnetic Field

We present a simple prescription to flatten isolated Bloch bands with a nonzero Chern number. We first show that approximate flattening of bands with a nonzero Chern number is possible by tuning ratios of nearest-neighbor and next-nearest-neighbor hoppings in the Haldane model and, similarly, in the chiral-π-flux square lattice model. Then we show that perfect flattening can be attained with further range hoppings that decrease exponentially with distance. Finally, we add interactions to the model and present exact diagonalization results for a small system at 1/3 filling that support (i) the existence of a spectral gap, (ii) that the ground state is a topological state, and (iii) that the Hall conductance is quantized.

Electron fractionalization in two-dimensional graphenelike structures

Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. In this Letter, we show that fractionally charged topological excitations exist on graphenelike structures, where quasiparticles are described by two flavors of Dirac fermions and time-reversal symmetry is respected. The topological zero modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics.

Two-dimensional conformal field theory for disordered systems at criticality

Using a Kac-Moody current algebra with U(1/1) × U(1/1) graded symmetry, we describe a class of (possibly disordered) critical points in two spatial dimensions. The critical points are labelled by the triplets (l, m, kj), where l is an odd integer, m is an integer, and kj is real. For most such critical points, we show that there are infinite hierarchies of relevant operators with negative scaling dimensions. To interpret this result, we show that the line of critical points (1, 1, kj > 0) is realized by a field theory of massless Dirac fermions in the presence of U(N) vector gauge-like static impurities. Along the disordered critical line (1, 1, kj > 0) we find an infinite hierarchy of relevant operators with negative scaling dimensions {δq∥q ϵ N}, which are related to the disorder average over the qth moment of the single-particle Green function. Those relevant operators can be induced by non-Gaussian moments of the probability distribution of a mass-like static disorder.

Liouville Theory as a Model for Prelocalized States in Disordered Conductors.

It is established that the distribution of the zero energy eigenfunctions of (

Localization in Two Dimensions, Gaussian Field Theories, and Multifractality.

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Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field

)-dimensional Dirac electrons in a random gauge potential is described by the Liouville model. This model has a line of critical points parametrized by the strength of disorder and the scaling dimensions of the inverse participation ratios coincide with the dimensions obtained in the conventional localization theory. From this fact we conclude that the renormalization group trajectory of the latter theory lies in the vicinity of the line of critical points of the Liouville model.

Fractional topological liquids with time-reversal symmetry and their lattice realization

The computation of multifractal scaling properties associated with a critical field theory involves non-local operators and remains an open problem using conventional techniques of field theory. We propose a new description of Gaussian field theories in terms of random Cantor sets and show how universal multifractal scaling exponents can be calculated. We use this approach to characterize the multifractal critical wave function of Dirac fermions interacting with a random vector potential in two spatial dimensions. We show that the multifractal scaling exponents are self-averaging.

Landauer conductance and twisted boundary conditions for Dirac fermions in two space dimensions

The multifractal scaling exponents are calculated for the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into the thermodynamics of a static particle in a random potential. The multifractal exponents are simply given in terms of thermodynamic functions, such as free energy and entropy, which are argued to be self-averaging in the thermodynamic limit. These thermodynamic functions are shown to coincide exactly with those of a Generalized Random Energy Model, in agreement with previous results obtained using Gaussian field theories in an ultrametric space.

Spin-glass state and long-range magnetic order in Pb ( Fe 1 / 2 Nb 1 / 2 ) O 3 seen via neutron scattering and muon spin rotation

We present a class of time-reversal-symmetric fractional topological liquid states in two dimensions that support fractionalized excitations. These are incompressible liquids made of electrons, for which the charge Hall conductance vanishes and the spin Hall conductance needs not be quantized. We then analyze the stability of edge states in these two-dimensional topological fluids against localization by disorder. We find a

DELOCALIZATION IN COUPLED ONE-DIMENSIONAL CHAINS

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