Energy transport in the Anderson insulator

TL;DR

This paper investigates heat conduction in Anderson insulators with power-law interactions, revealing how energy propagates through resonant networks of localized states and deriving temperature-dependent thermal conductivity in 2D and 3D systems.

Contribution

It introduces a model of energy transport via resonant pairs of localized states in Anderson insulators with long-range interactions, providing new scaling laws for thermal conductivity.

Findings

Thermal conductivity scales as T^3 in 2D systems.

Thermal conductivity scales as T^{4/3} in 3D systems.

Energy transport occurs through a network of resonant pairs of localized states.

Abstract

We study the heat conductivity in Anderson insulators in the presence of power-law interaction. Particle-hole excitations built on localized electron states are viewed as two-level systems randomly distributed in space and energy and coupled due to electron-electron interaction. A small fraction of these states form resonant pairs that in turn build a complex network allowing for energy propagation. We identify the character of energy transport through this network and evaluate the thermal conductivity. For physically relevant cases of 2D and 3D spin systems with $1/r^3$ dipole-dipole interaction (originating from the conventional $1/r$ Coulomb interaction between electrons), the found thermal conductivity $\kappa$ scales with temperature as $\kappa\propto T^3 $ and $\kappa\propto T^{4/3}$, respectively. Our results may be of relevance also to other realizations of random spin Hamiltonians with long-range interactions.