Modeling Disordered Quantum Systems with Dynamical Networks

TL;DR

This paper extends static network models of disordered electronic systems to dynamical models, enabling the study of quantum dynamics, spectral properties, and conductance, with applications demonstrated on quantum Hall and metal-insulator transition models.

Contribution

It introduces a generalization of network models to quantum dynamical systems, facilitating analysis of spectral and dynamical properties in disordered quantum systems.

Findings

Simulated phase coherent diffusion of wave packets.

Analyzed spectral correlations and energy level distributions.

Determined an anomalous diffusion exponent of approximately 1.7.

Abstract

It is the purpose of the present article to show that so-called network models, originally designed to describe static properties of disordered electronic systems, can be easily generalized to quantum-{\em dynamical} models, which then allow for an investigation of dynamical and spectral aspects. This concept is exemplified by the Chalker-Coddington model for the Quantum Hall effect and a three-dimensional generalization of it. We simulate phase coherent diffusion of wave packets and consider spatial and spectral correlations of network eigenstates as well as the distribution of (quasi-)energy levels. Apart from that it is demonstrated how network models can be used to determine two-point conductances. Our numerical calculations for the three-dimensional model at the Metal-Insulator transition point delivers among others an anomalous diffusion exponent of $\eta = 3 - D_2 = 1.7 \pm 0.1$. The methods presented here in detail have been used partially in earlier work.