{
  "id": "1802.08393",
  "version": "v1",
  "published": "2018-02-23T05:32:23.000Z",
  "updated": "2018-02-23T05:32:23.000Z",
  "title": "Boltzmann transport theory for many body localization",
  "authors": [
    "Jae-Ho Han",
    "Ki-Seok Kim"
  ],
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.str-el"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-23T05:32:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "many-body localization transition",
      "diffusion coefficient",
      "wolfle-vollhardt self-consistent equation",
      "boltzmann equation",
      "three-dimensional metal-insulator transition differs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}