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Metalinsulator transition in a weakly interacting manyelectron system with localized singleparticle states

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Author:  D.M. Basko, I.L. Aleiner, B.L. Altshuler 
















Description 
We consider lowtemperature behavior of weakly interacting electrons in disordered conductors in the regime when all singleparticle eigenstates are localized by the quenched disorder. We prove that in the absence of coupling of the electrons to any external bath dc electrical conductivity exactly vanishes as long as the temperatute 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 MetaltoInsulator transition, which can be viewed as Andersonlike localization of manybody wave functions in the Fock space. Metallic and insulating states are not different from each other by any spatial or discrete symmetries. We formulate the effective Hamiltonian description of the system at low energies (of the order of the level spacing in the singleparticle localization volume). In the metallic phase quantum Boltzmann equation is valid, allowing to find the kinetic coefficients. In the insulating phase, T<Tc, we use Feynmann diagram technique to determine the probability distribution function for quantummechanical transition rates. The probability of an escape rate from a given quantum state to be finite turns out to vanish in every order of the perturbation theory in electronelectron interaction. Thus, electronelectron interaction alone is unable to cause the relaxation and establish the thermal equilibrium. As soon as some weak coupling to a bath is turned on, conductivity becomes finite even in the insulating phase. 

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