{
  "id": "1908.06643",
  "version": "v1",
  "published": "2019-08-19T08:41:59.000Z",
  "updated": "2019-08-19T08:41:59.000Z",
  "title": "Taming two interacting particles with disorder",
  "authors": [
    "Diana Thongjaomayum",
    "Alexei Andreanov",
    "Thomas Engl",
    "Sergej Flach"
  ],
  "comment": "4 pages, 4 figures",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We compute the scaling properties of the localization length $\\xi_2$ of two interacting particles in a one-dimensional chain with diagonal disorder, and the connectivity properties of the Fock states. We analyze record large system sizes (up to $N=20000$) and disorder strengths (down to $W=0.5$). We vary the energy $E$ and the on-site interaction strength $u$. At a given disorder strength the largest enhancement of $\\xi_2$ occurs for $u$ of the order of the single particle band width, and for two-particle states with energies at the center of the spectrum, $E=0$. We observe a crossover in the scaling of $\\xi_2$ with the single particle localization length $\\xi_1$ into the asymptotic regime for $\\xi_1 > 100$ ($W < 1.0$). This happens due to the recovery of translational invariance and momentum conservation rules in the matrix elements of interconnected Fock eigenstates for $u=0$. The entrance into the asymptotic scaling is manifested through a nonlinear scaling function $\\xi_2/\\xi_1=F(u\\xi_1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-19T08:41:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "interacting particles",
      "analyze record large system sizes",
      "disorder strength",
      "single particle band width",
      "single particle localization length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}