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Physical review. B, Condensed matter

Correlation corrections to the conductivity of one-dimensional disordered hopping models

Radu Pitiş, P. Gärtner

Published May 1, 1991• 9 citations
Publisher

Abstract

Transport on a one-dimensional nonuniform periodic chain with a hard-core interaction is examined. The mean-field conductivity is rederived, and the first correction due to many-particle effects is obtained. By letting the period go to infinity, the results are extended to nonperiodic chains, including the random one. The case of the site-disordered system with two values of the site energy is discussed in detail.

DOI
10.1103/physrevb.43.11294

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Transport on a one-dimensional nonuniform periodic chain with a hard-core interaction is examined. The mean-field conductivity is rederived, and the first correction due to many-particle effects is obtained. By letting the period go to infinity, the results are extended to nonperiodic chains, including the random one. The case of the site-disordered system with two values of the site energy is discussed in detail.
Abstract We study the transport properties of a one-dimensional quantum system with disorder. We numerically compute the frequency dependence of the conductivity of a fermionic chain with nearest-neighbor interaction and a random chemical potential by using the Chebyshev matrix product state (CheMPS) method. As a benchmark, we investigate the noninteracting case first. Comparison with exact diagonalization and analytical solutions demonstrates that the results of CheMPS are reliable over a wide range of frequencies. We then calculate the dynamical conductivity spectra of the interacting system for various values of the interaction and disorder strengths. In the high-frequency regime, the conductivity decays as a power law, with an interaction-dependent exponent. This behavior is qualitatively consistent with the bosonized field theory predictions, although the numerical evaluation of the exponent shows deviations from the analytically expected values. We also compute the characteristic pinning frequency at which a peak in the conductivity appears. We confirm that it is directly related to the inverse of the localization length, even in the interacting case. We demonstrate that the localization length follows a power law of the disorder strength with an exponent dependent on the interaction, and find good quantitative agreement with the field theory predictions. In the low-frequency regime, we find a behavior consistent with the one of the noninteracting system ω2(ln⁡ω)2\omega ^{2}(\ln \omega )^{2}ω2(lnω)2 ω 2 ( ln ω ) 2 independently of the interaction. We discuss the consequences of our finding for experiments in cold atomic gases. Graphical abstract
We study the spin transport properties of some disordered spin chains with a special focus on the distribution of the frequency-dependent spin conductivity. In the cases of interest here, the systems are governed by an effectively infinite disorder at low energies. A hallmark of this behavior is the wide discrepancy between the average and the typical values of some physical quantities, which are described by extremely broad distributions. We show that such is also the case of the spin conductivity, whose average value is metallic but whose typical one, the physically relevant quantity, is insulating. This solves the apparent contradiction between the prediction of a spin metallic phase of the spin-1/2 disordered XX chain and its known localized behavior (after a mapping to free fermions). Our results are based on analytical and numerical implementations of a strong-disorder renormalization group as well as exact diagonalization studies. We present our analyses in very general terms, valid for systems of any spin SSS value, but the cases of S=1/2S=1/2S=1/2 and 1 are studied in greater detail.
We study the strong correlation effects in the vicinity of the Mott metal-insulator transition using coupled clean or disordered Hubbard chains with a infinitely large coordinate number D⊥→∞D_{\perp}\to\inftyD⊥​→∞ in the direction perpendicular to the chains and with a long-range transverse hopping. Strong electron correlation effects are treated partially non-perturbatively with the use of the exact results for the 1D Hubbard model. In the case of clean systems, the thermodynamic and transport quantities which characterize the Mott transition from the Fermi liquid state, such as the specific heat coefficient, the Drude weight, and the compressibility, are obtained as functions of hole-doping δ=1−nδ=1-nδ=1−n (nnn, electron density) by the systematic expansion in terms of the inverse of the transverse hopping range l⊥l_{\perp}l⊥​. We find that the δδδ-dependence of these quantities shows non-universal behaviors with exponents depending on the strength of electron-electron interaction. In the presence of disorder, it is shown that the frequency-dependence of the dynamical conductivity obeys the Mott's law, implying the possibility of {\it Mott glass state} for δ→0δ\to 0δ→0, provided that there exists a finite range interaction.
We numerically investigate the transport properties of disordered interacting electrons in three dimensions in the metallic as well as in the insulating phases. The disordered many-particle problem is modeled by the quantum Coulomb glass which contains a random potential, long-range unscreened Coulomb interactions and quantum hopping between different sites. We have recently developed the Hartree-Fock based diagonalization (HFD) method which amounts to diagonalizing the Hamiltonian in a suitably chosen energetically truncated basis. This method allows us to investigate comparatively large systems. Here we calculate the combined effect of disorder and interactions on the dissipative conductance. We find that the qualitative influence of the interactions on the conductance depends on the relative disorder strength. For strong disorder interactions can significantly enhance the transport while they suppress the conductance for weak disorder.
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