Boltzmann transport theory for many body localization

Jae-Ho Han, Ki-Seok Kim

Published 2018-02-23Version 1

We investigate a many-body localization transition based on a Boltzmann transport theory. Introducing weak localization corrections into a Boltzmann equation and taking into account self-consistency for a diffusion coefficient, the Wolfle-Vollhardt self-consistent equation for the diffusion coefficient has been derived, which describes an Anderson metal-insulator transition in a continuous fashion [Phys. Rev. B {\bf 34}, 2147 (1986)]. We generalize this Boltzmann equation framework, introducing electron-electron interactions into the Hershfield-Ambegaokar Boltzmann transport theory based on the study of Zala-Narozhny-Aleiner [Phys. Rev. B {\bf 64}, 214204 (2001)], where not only Altshuler-Aronov corrections but also dephasing effects are taken into account. As a result, we obtain a self-consistent equation for the diffusion coefficient in terms of the disorder strength and temperature, which extends the Wolfle-Vollhardt self-consistent equation in the presence of electron correlations. Solving our self-consistent equation numerically, we find a many-body localization insulator-metal transition, where a metallic phase appears from dephasing effects dominantly instead of renormalization effects at high temperatures. Although the mechanism for the many-body localization transition is consistent with that of recent seminal papers [Ann. Phys. (N. Y). {\bf 321}, 1126 (2006); Phys. Rev. Lett. {\bf 95}, 206603 (2005)], we find that nature of this three-dimensional metal-insulator transition differs from all of the previous studies in one dimension. We discuss the nature of our many-body localization transition carefully.