Chebyshev expansion approach to the AC conductivity of the Anderson model

TL;DR

This paper introduces a Chebyshev expansion method for efficiently calculating the optical conductivity of non-interacting electrons in disordered systems, revealing disorder-dependent power-law behavior near the metal-insulator transition.

Contribution

It develops a stable, resource-efficient Chebyshev approach for finite-temperature linear response calculations applicable to large disordered quantum systems.

Findings

Power-law behavior of conductivity at low frequencies.

Minimum exponent near the metal-insulator transition.

DC conductivity approaches zero at the transition.

Abstract

We propose an advanced Chebyshev expansion method for the numerical calculation of linear response functions at finite temperature. Its high stability and the small required resources allow for a comprehensive study of the optical conductivity $\sigma(\omega)$ of non-interacting electrons in a random potential (Anderson model) on large three-dimensional clusters. For low frequency the data follows the analytically expected power-law behaviour with an exponent that depends on disorder and has its minimum near the metal-insulator transition, where also the extrapolated DC conductivity continuously goes to zero. In view of the general applicability of the Chebyshev approach we briefly discuss its formulation for interacting quantum systems.