Finite temperature metal-insulator transition in an interacting many-electron system

Igor Aleiner

Physics Department, Columbia University, New York, USA

We consider low temperature behavior of weakly interacting electrons in disordered conductors in the regime when all single-particle eigenstates are localized by the quenched disorder. We prove that in the absence of coupling of the electrons to an external bath dc electrical conductivity exactly vanishes as long as the temperature T does not exceed some finite value Tc. At the same time, it can be also proven that at high enough T the conductivity is finite. These two statements imply that the system undergoes a finite temperature Metal-to-Insulator transition, which can be viewed as Anderson-like localization of many-body wave functions in the Fock space. Metallic and insulating states are not different from each other by any spatial or discrete symmetries.