{
  "id": "2107.06364",
  "version": "v1",
  "published": "2021-07-13T20:00:30.000Z",
  "updated": "2021-07-13T20:00:30.000Z",
  "title": "Scaling Theory of Few-Particle Delocalization",
  "authors": [
    "Louk Rademaker"
  ],
  "comment": "9 pages, 2 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.quant-gas",
    "cond-mat.str-el"
  ],
  "abstract": "We develop a scaling theory of interaction-induced delocalization of few-particle states in disordered quantum systems. In the absence of interactions, all single-particle states are localized in $d<3$, while in $d \\geq 3$ there is a critical disorder below which states are delocalized. We hypothesize that such a delocalization transition occurs for $n$-particle bound states in $d$ dimensions when $d+n\\geq 4$. Exact calculations of disorder-averaged $n$-particle Greens functions support our hypothesis. In particular, we show that $3$-particle states in $d=1$ with nearest-neighbor repulsion will delocalize with $W_c \\approx 1.4t$ and with localization length critical exponent $\\nu = 1.5 \\pm 0.3$. The delocalization transition can be understood by means of a mapping onto a non-interacting problem with symplectic symmetry. We discuss the importance of this result for many-body delocalization, and how few-body delocalization can be probed in cold atom experiments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-13T20:00:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scaling theory",
      "few-particle delocalization",
      "particle greens functions support",
      "particle bound states",
      "delocalization transition occurs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}