Delocalization and energy transport in a many-body system with power-law interaction

I will discuss the delocalization and heat transport in a many-body system due to a power-law interaction. One experimentally relevant realization of this problem is the effect of Coulomb interaction in Anderson insulators. In particular, experiments demonstrating efficient heat transport through the bulk of quantum Hall systems served as a motivation for this work. Particle-hole excitations built on localized electron states are viewed as two-level systems (“spins”) 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 and evaluate the spin relaxation rate and the thermal conductivity. For physically relevant cases of two-dimensional and three-dimensional “spin" systems with 1/r^{3} dipole-dipole interaction (originating from the conventional 1/r Coulomb interaction between electrons), the found thermal conductivity κ scales with temperature as κ ∝ T^{3} and κ ∝ T^{4/3}, respectively. Our results are of relevance also to other realizations of random spin Hamiltonians with long-range interactions. We also determine the delocalization threshold for a finite-size system (“quantum dot” with localized single-particle states and power-law interaction). In this context, I will discuss a connection of this problem with Anderson localization on random regular graphs.