Sufficient Conditions for Topological Order in Insulators

We prove the existence of low energy excitations in insulating systems at general filling factor under certain conditions, and discuss in which cases these may be identified as topological excitations. This proof is based on previously proven locality results. In the case of half-filling it provides a significantly shortened proof of the recent higher dimensional Lieb-Schultz-Mattis theorem.Comment: 7 pages, no figure

Absence of localization in a disordered one-dimensional ring threaded by an Aharonov-Bohm flux

Absence of localization is demonstrated analytically to leading order in weak disorder in a one-dimensional Anderson model of a ring threaded by an Aharonov-Bohm (A-B) flux. The result follows from adapting an earlier perturbation treatment of disorder in a superconducting ring subjected to an imaginary vector potential proportional to a depinning field for flux lines bound to random columnar defects parallel to the axis of the ring. The absence of localization in the ring threaded by an A-B flux for sufficiently weak disorder is compatible with large free electron type persistent current obtained in recent studies of the above model

Realistic model of correlated disorder and Anderson localization

A conducting 1D line or 2D plane inside (or on the surface of) an insulator is considered.Impurities displace the charges inside the insulator. This results in a long-range fluctuating electric field acting on the conducting line (plane). This field can be modeled by that of randomly distributed electric dipoles. This model provides a random correlated potential with decaying as 1/k . In the 1D case such correlations give essential corrections to the localization length but do not destroy Anderson localization

Ensemble Averaged Conductance Fluctuations in Anderson Localized Systems

We demonstrate the presence of energy dependent fluctuations in the localization length, which depend on the disorder distribution. These fluctuations lead to Ensemble Averaged Conductance Fluctuations (EACF) and are enhanced by large disorder. For the binary distribution the fluctuations are strongly enhanced in comparison to the Gaussian and uniform distributions. These results have important implications on ensemble averaged quantities, such as the transmission through quantum wires, where fluctuations can subsist to very high temperatures. For the non-fluctuating part of the localization length in one dimension we obtained an improved analytical expression valid for all disorder strengths by averaging the probability density.Comment: 4 page

The Complexity of Vector Spin Glasses

We study the annealed complexity of the m-vector spin glasses in the Sherrington-Kirkpatrick limit. The eigenvalue spectrum of the Hessian matrix of the Thouless-Anderson-Palmer (TAP) free energy is found to consist of a continuous band of positive eigenvalues in addition to an isolated eigenvalue and (m-1) null eigenvalues due to rotational invariance. Rather surprisingly, the band does not extend to zero at any finite temperature. The isolated eigenvalue becomes zero in the thermodynamic limit, as in the Ising case (m=1), indicating that the same supersymmetry breaking recently found in Ising spin glasses occurs in vector spin glasses.Comment: 4 pages, 2 figure

Stability of the shell structure in 2D quantum dots

We study the effects of external impurities on the shell structure in semiconductor quantum dots by using a fast response-function method for solving the Kohn-Sham equations. We perform statistics of the addition energies up to 20 interacting electrons. The results show that the shell structure is generally preserved even if effects of high disorder are clear. The Coulomb interaction and the variation in ground-state spins have a strong effect on the addition-energy distributions, which in the noninteracting single-electron picture correspond to level statistics showing mixtures of Poisson and Wigner forms.Comment: 7 pages, 8 figures, submitted to Phys. Rev.

Berry phase and quantized Hall effect in three-dimension

We consider Bloch electrons in the electromagnetic field and argue the relation between the Berry phase and the quantized Hall conductivity in three-dimension. The Berry phase we consider here is induced by the adiabatic change of the time-dependent vector potential. The relation has been shown in two-dimensional systems, and we generalize the relation in three-dimensional systems.Comment: corrected some typos. Accepted for publication in J. Phys. Soc. Jp

Conductance and localization in disordered wires: role of evanescent states

This paper extends an earlier analytical scattering matrix treatment of conductance and localization in coupled two- and three Anderson chain systems for weak disorder when evanescent states are present at the Fermi level. Such states exist typically when the interchain coupling exceeds the width of propagating energy bands associated with the various transverse eigenvalues of the coupled tight-binding systems. We calculate reflection- and transmission coefficients in cases where, besides propagating states, one or two evanescent states are available at the Fermi level for elastic scattering of electrons by the disordered systems. We observe important qualitative changes in these coefficients and in the related localization lengths due to ineffectiveness of the evanescent modes for transmission and reflection in the various scattering channels. In particular, the localization lengths are generally significantly larger than the values obtained when evanescent modes are absent. Effects associated with disorder mediated coupling between propagating and evanescent modes are shown to be suppressed by quantum interference effects, in lowest order for weak disorder

Saddle index properties, singular topology, and its relation to thermodynamical singularities for a phi^4 mean field model

We investigate the potential energy surface of a phi^4 model with infinite range interactions. All stationary points can be uniquely characterized by three real numbers $\alpha_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_- = 1, provided that the interaction strength mu is smaller than a critical value. The saddle index n_s is equal to alpha_0 and its distribution function has a maximum at n_s^max = 1/3. The density p(e) of stationary points with energy per particle e, as well as the Euler characteristic chi(e), are singular at a critical energy e_c(mu), if the external field H is zero. However, e_c(mu) \neq upsilon_c(mu), where upsilon_c(mu) is the mean potential energy per particle at the thermodynamic phase transition point T_c. This proves that previous claims that the topological and thermodynamic transition points coincide is not valid, in general. Both types of singularities disappear for H \neq 0. The average saddle index bar{n}_s as function of e decreases monotonically with e and vanishes at the ground state energy, only. In contrast, the saddle index n_s as function of the average energy bar{e}(n_s) is given by n_s(bar{e}) = 1+4bar{e} (for H=0) that vanishes at bar{e} = -1/4 > upsilon_0, the ground state energy.Comment: 9 PR pages, 6 figure