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

I will discuss the delocalization 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. 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.