Interacting electrons in disordered wires: Anderson localization and low-temperature transport

We study transport of interacting electrons in a low-dimensional disordered system at low temperature $T$. In view of localization by disorder, the conductivity $sigma(T)$ may only be non-zero due to electron-electron scattering. For weak interactions, the weak-localization regime crosses over with lowering $T$ into a dephasing-induced power-law hopping. As $T$ is further decreased, the Anderson localization in Fock space crucially affects $sigma(T)$, inducing a transition at $T=T_c$, so that $sigma(T<T_c)=0$. The critical behavior of $sigma(T)$ above $T_c$ is $lnsigma(T)propto - (T-T_c)^{-1/2}$. The mechanism of transport in the critical regime is many-particle transitions between distant states in Fock space.