Dynamical Conductivity of One-dimensional Disordered Interacting Fermions

Michael Dzierzawa, K. Schl�ter

Walter Lehr

O. S. Barišić, Peter Prelovšek

Dynamical conductivity in a disordered one-dimensional model of interacting fermions is studied numerically at high temperatures and in the weak-interaction regime in order to find a signature of many-body localization and vanishing dc transport coefficients. On the contrary, we find in the regime of moderately strong local disorder that the dc conductivity ${\ensuremath{\sigma}}_{0}$ scales linearly with the interaction strength while being exponentially dependent on the disorder. According to the behavior of the charge stiffness evaluated at the fixed number of particles, the absence of the many-body localization seems related to an increase in the effective localization length with the interaction.

Jean-Philippe Brantut

W. Apel, Thomas Maurice Rice

It is shown that the conductance of an interacting one-dimensional system may be expressed in the form of a Landauer formula. An insulator-ideal-conductor transition is found as the interaction is varied at zero temperature.

A. A. Dontsov, D. N. Aristov, А. П. Дмитриев

We analyze the uniform conductivity of a one-dimensional degenerate fermion system placed in a random disorder potential so smooth that backward scattering can be neglected. We use the nonlinear Luttinger liquid model to consider effects of both interaction and the curvature of fermionic dispersion. The finite frequency conductivity, calculated in the lowest order of disorder potential, consists of two parts. First one is the elastic contribution, largely independent of temperature and interaction. Second one is the inelastic contribution, strongly dependent on temperature and frequency and appearing upon simultaneous presence of curvature, disorder and interaction. We argue that apart from such finite frequency conductivity, there should always remain the $δ$-function peak of conductivity at zero frequency, whose weight is weakly dependent on the disorder.