Enhancing the stability of a fractional Chern insulator against competing phases

We construct a two-band lattice model whose bands can carry the Chern numbers C=0,pm1,pm2. By means of numerical exact diagonalization, we show that the most favorable situation that selects fractional Chern insulators (FCIs) is not necessarily the one that mimics Landau levels, namely a flat band with Chern number 1. First, we find that the gap, measured in units of the on-site electron-electron repulsion, can increase by almost two orders of magnitude when the bands are flat and carry a Chern number C=2 instead of C=1. Second, we show that giving a width to the bands can help to stabilize a FCI. Finally, we put forward a tool to characterize the real-space density profile of the ground state that is useful to distinguish FCI from other competing phases of matter supporting charge density waves or phase separation.Comment: 10 pages, 6 figure

Noncommutative geometry for three-dimensional topological insulators

We generalize the noncommutative relations obeyed by the guiding centers in the two-dimensional quantum Hall effect to those obeyed by the projected position operators in three-dimensional (3D) topological band insulators. The noncommutativity in 3D space is tied to the integral over the 3D Brillouin zone of a Chern-Simons invariant in momentum-space. We provide an example of a model on the cubic lattice for which the chiral symmetry guarantees a macroscopic number of zero-energy modes that form a perfectly flat band. This lattice model realizes a chiral 3D noncommutative geometry. Finally, we find conditions on the density-density structure factors that lead to a gapped 3D fractional chiral topological insulator within Feynman's single-mode approximation.Comment: 41 pages, 3 figure

Excitation spectrum of the homogeneous spin liquid

We discuss the excitation spectrum of a disordered, isotropic and translationally invariant spin state in the 2D Heisenberg antiferromagnet. The starting point is the nearest-neighbor RVB state which plays the role of the vacuum of the theory, in a similar sense as the Neel state is the vacuum for antiferromagnetic spin wave theory. We discuss the elementary excitations of this state and show that these are not Fermionic spin-1/2 `spinons' but spin-1 excited dimers which must be modeled by bond Bosons. We derive an effective Hamiltonian describing the excited dimers which is formally analogous to spin wave theory. Condensation of the bond-Bosons at zero temperature into the state with momentum (pi,pi) is shown to be equivalent to antiferromagnetic ordering. The latter is a key ingredient for a microscopic interpretation of Zhang's SO(5) theory of cuprate superconductivityComment: RevTex-file, 16 PRB pages with 13 embedded eps figures. Hardcopies of figures (or the entire manuscript) can be obtained by e-mail request to: [email protected]

Zero-modes in the random hopping model

If the number of lattice sites is odd, a quantum particle hopping on a bipartite lattice with random hopping between the two sublattices only is guaranteed to have an eigenstate at zero energy. We show that the localization length of this eigenstate depends strongly on the boundaries of the lattice, and can take values anywhere between the mean free path and infinity. The same dependence on boundary conditions is seen in the conductance of such a lattice if it is connected to electron reservoirs via narrow leads. For any nonzero energy, the dependence on boundary conditions is removed for sufficiently large system sizes.Comment: 12 pages, 11 figure

Conductance scaling at the band center of wide wires with pure non--diagonal disorder

Kubo formula is used to get the scaling behavior of the static conductance distribution of wide wires showing pure non-diagonal disorder. Following recent works that point to unusual phenomena in some circumstances, scaling at the band center of wires of odd widths has been numerically investigated. While the conductance mean shows a decrease that is only proportional to the inverse square root of the wire length, the median of the distribution exponentially decreases as a function of the square root of the length. Actually, the whole distribution decays as the inverse square root of the length except close to G=0 where the distribution accumulates the weight lost at larger conductances. It accurately follows the theoretical prediction once the free parameter is correctly fitted. Moreover, when the number of channels equals the wire length but contacts are kept finite, the conductance distribution is still described by the previous model. It is shown that the common origin of this behavior is a simple Gaussian statistics followed by the logarithm of the E=0 wavefunction weight ratio of a system showing chiral symmetry. A finite value of the two-dimensional conductance mean is obtained in the infinite size limit. Both conductance and the wavefunction statistics distributions are given in this limit. This results are consistent with the 'critical' character of the E=0 wavefunction predicted in the literature.Comment: 10 pages, 9 figures, RevTeX macr

Spectral Statistics in Chiral-Orthogonal Disordered Systems

We describe the singularities in the averaged density of states and the corresponding statistics of the energy levels in two- (2D) and three-dimensional (3D) chiral symmetric and time-reversal invariant disordered systems, realized in bipartite lattices with real off-diagonal disorder. For off-diagonal disorder of zero mean we obtain a singular density of states in 2D which becomes much less pronounced in 3D, while the level-statistics can be described by semi-Poisson distribution with mostly critical fractal states in 2D and Wigner surmise with mostly delocalized states in 3D. For logarithmic off-diagonal disorder of large strength we find indistinguishable behavior from ordinary disorder with strong localization in any dimension but in addition one-dimensional $1/|E|$ Dyson-like asymptotic spectral singularities. The off-diagonal disorder is also shown to enhance the propagation of two interacting particles similarly to systems with diagonal disorder. Although disordered models with chiral symmetry differ from non-chiral ones due to the presence of spectral singularities, both share the same qualitative localization properties except at the chiral symmetry point E=0 which is critical.Comment: 13 pages, Revtex file, 8 postscript files. It will appear in the special edition of J. Phys. A for Random Matrix Theor

Random Dirac Fermions and Non-Hermitian Quantum Mechanics

We study the influence of a strong imaginary vector potential on the quantum mechanics of particles confined to a two-dimensional plane and propagating in a random impurity potential. We show that the wavefunctions of the non-Hermitian operator can be obtained as the solution to a two-dimensional Dirac equation in the presence of a random gauge field. Consequences for the localization properties and the critical nature of the states are discussed.Comment: 5 pages, Latex, 1 figure, version published in PR

The effects of weak disorders on Quantum Hall critical points

We study the consequences of random mass, random scalar potential and random vector potential on the line of clean fixed points between integer/fractional quantum Hall states and an insulator. This line of fixed points was first identified in a clean Dirac fermion system with both Chern-Simon coupling and Coulomb interaction in Phys. Rev. Lett. {\bf 80}, 5409 (1998). By performing a Renormalization Group analysis in 1/N (N is the No. of species of Dirac fermions) and the variances of three disorders $\Delta_{M}, \Delta_{V}, \Delta_{A}$, we find that $\Delta_{M}$ is irrelevant along this line, both $\Delta_{A}$ and $\Delta_{V}$ are marginal. With the presence of all the three disorders, the pure fixed line is unstable. Setting Chern-Simon interaction to zero, we find one non-trivial line of fixed points in $(\Delta_{A}, w)$ plane with dynamic exponent z=1 and continuously changing $\nu$, it is stable against small $(\Delta_{M},\Delta_{V})$ in a small range of the line $1< w < 1.31$, therefore it may be relevant to integer quantum Hall transition. Setting $\Delta_{M} =0$, we find a fixed plane with z=1, the part of this plane with $\nu > 1$ is stable against small $\Delta_{M}$, therefore it may be relevant to fractional quantum Hall transition.Comment: 16 pages, 19 figure

Density of states in the non-hermitian Lloyd model

We reconsider the recently proposed connection between density of states in the so-called ``non-hermitian quantum mechanics'' and the localization length for a particle moving in random potential. We argue that it is indeed possible to find the localization length from the density of states of a non-hermitian random ``Hamiltonian''. However, finding the density of states of a non-hermitian random ``Hamiltonian'' remains an open problem, contrary to previous findings in the literature.Comment: 6 pages, RevTex, two-column

Confinement of Slave-Particles in U(1) Gauge Theories of Strongly-Interacting Electrons

We show that slave particles are always confined in U(1) gauge theories of interacting electron systems. Consequently, the low-lying degrees of freedom are different from the slave particles. This is done by constructing a dual formulation of the slave-particle representation in which the no-double occupany constraint becomes linear and, hence, soluble. Spin-charge separation, if it occurs, is due to the existence of solitons with fractional quantum numbers