Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at E=0E=0 without Doubling

Random bond Hamiltonians of the $\pi$ flux state on the square lattice are investigated. It has a special symmetry and all states are paired except the ones with zero energy. Because of this, there are always zero-modes. The states near $E=0$ are described by massless Dirac fermions. For the zero-mode, we can construct a random lattice fermion without a doubling and quite large systems ( up to $801 \times 801$) are treated numerically. We clearly demonstrate that the zero-mode is given by a critical wave function. Its multifractal behavior is also compared with the effective field theory.Comment: 4 pages, 2 postscript figure

Disorder Effects in Two-Dimensional d-wave Superconductors

Influence of weak nonmagnetic impurities on the single-particle density of states $\rho(\omega)$ of two-dimensional electron systems with a conical spectrum is studied. We use a nonperturbative approach, based on replica trick with subsequent mapping of the effective action onto a one-dimensional model of interacting fermions, the latter being treated by Abelian and non-Abelian bosonization methods. It is shown that, in a d-wave superconductor, the density of states, averaged over randomness, follows a nontrivial power-law behavior near the Fermi energy: $\rho(\omega) \sim |\omega|^{\alpha}$. The exponent $\alpha>0$ is calculated for several types of disorder. We demonstrate that the property $\rho(0) = 0$ is a direct consequence of a {\it continuous} symmetry of the effective fermionic model, whose breakdown is forbidden in two dimensions. As a counter example, we consider another model with a conical spectrum - a two-dimensional orbital antiferromagnet, where static disorder leads to a finite $\rho(0)$ due to breakdown of a {\it discrete} (particle-hole) symmetry.Comment: 24 pages, 3 figures upon request, RevTe

Scaling near random criticality in two-dimensional Dirac fermions

Recently the existence of a random critical line in two dimensional Dirac fermions is confirmed. In this paper, we focus on its scaling properties, especially in the critical region. We treat Dirac fermions in two dimensions with two types of randomness, a random site (RS) model and a random hopping (RH) model. The RS model belongs to the usual orthogonal class and all states are localized. For the RH model, there is an additional symmetry expressed by ${\{}{\cal H},{\gamma}{\}}=0$. Therefore, although all non-zero energy states localize, the localization length diverges at the zero energy. In the weak localization region, the generalized Ohm's law in fractional dimensions, $d^{*}(<2)$, has been observed for the RH model.Comment: RevTeX with 4 postscript figures, To appear in Physical Review

Impurity effects in unconventional density waves in the unitary limit

We investigate the effect of strong, nonmagnetic impurities on quasi-one-dimensional conventional and unconventional density waves (DW and UDW). The conventional case remains unaffected similarly to s-wave superconductors in the presence of weak, nonmagnetic impurities. The thermodynamic properties of UDW were found to be identical to those of a d-wave superconductor in the unitary limit. The real and imaginary part of the optical conductivity is determined for electric fields applied in the perpendicular directions. A new structure can be present corresponding to excitations from the bound state at the Fermi energy to the gap maximum in addition to the usual peak at 2\Delta. In the dc limit, universal electric conductivity is found.Comment: 9 pages, 5 figure

Dynamical Chiral Symmetry Breaking in Unquenched QED3{QED}_3

We investigate dynamical chiral symmetry breaking in unquenched ${QED}_3$ using the coupled set of Dyson--Schwinger equations for the fermion and photon propagators. For the fermion-photon interaction we employ an ansatz which satisfies its Ward--Green--Takahashi identity. We present self-consistent analytical solutions in the infrared as well as numerical results for all momenta. In Landau gauge, we find a phase transition at a critical number of flavours of $N_f^{\mathrm crit} \approx 4$. In the chirally symmetric phase the infrared behaviour of the propagators is described by power laws with interrelated exponents. For $N_f=1$ and $N_f=2$ we find small values for the chiral condensate in accordance with bounds from recent lattice calculations. We investigate the Dyson--Schwinger equations in other linear covariant gauges as well. A comparison of their solutions to the accordingly transformed Landau gauge solutions shows that the quenched solutions are approximately gauge covariant, but reveals a significant amount of violation of gauge covariance for the unquenched solutions.Comment: 33 pages, 8 figures, reference added, version to be published in Phys. Rev.

Impurity scattering in unconventional density waves

We have investigated the effect of nonmagnetic impurities on the quasi-one-dimensional unconventional density wave (UDW) ground state. The thermodynamics were found to be close to those of a d-wave superconductor in the Born limit. Four different optical conductivity curves were found depending on the direction of the applied electric field and on the wavevector dependence of the gap.Comment: 14 pages, 9 figure

The fate of spinons in spontaneously dimerised spin-1/2 ladders

We study a weakly coupled, frustrated two-leg spin-1/2 Heisenberg ladder. For vanishing coupling between the chains, elementary excitations are deconfined, gapless spin-1/2 objects called spinons. We investigate the fate of spinons for the case of a weak interchain interaction. We show that despite a drastic change in ground state, which becomes spontaneously dimerised, spinons survive as elementary excitations but acquire a spectral gap. We furthermore determine the exact dynamical structure factor for several values of momentum transfer.Comment: 8 pages of revtex, 7 figures; discussion of physical picture for ground state and excitations in the "twistless" ladder expanded, version to appear in Phys Rev

Plateaux Transitions in the Pairing Model:Topology and Selection Rule

Based on the two-dimensional lattice fermion model, we discuss transitions between different pairing states. Each phase is labeled by an integer which is a topological invariant and characterized by vortices of the Bloch wavefunction. The transitions between phases with different integers obey a selection rule. Basic properties of the edge states are revealed. They reflect the topological character of the bulk. Transitions driven by randomness are also discussed numerically.Comment: 8 pages with 2 postscript figures, RevTe

Quasiparticle Localization in Disordered d-Wave Superconductors

An extensive numerical study is reported on disorder effect in two-dimensional d-wave superconductors with random impurities in the unitary limit. It is found that a sharp resonant peak shows up in the density of states at zero energy and correspondingly the finite-size spin conductance is strongly enhanced which results in a non-universal feature in one-parameter scaling. However, all quasiparticle states remain localized, indicating that the resonant density peak alone is not sufficient to induce delocalization. In the weak disorder limit, the localization length is so long that the spin conductance at small sample size is close to the universal value predicted by Lee (Phys. Rev. Lett. {\bf 71}, 1887 (1993)).Comment: 4 pages, 3 figure