{
  "id": "2407.04132",
  "version": "v1",
  "published": "2024-07-04T19:35:40.000Z",
  "updated": "2024-07-04T19:35:40.000Z",
  "title": "The integer quantum Hall transition: an $S$-matrix approach to random networks",
  "authors": [
    "Hrant Topchyan",
    "Ilya Gruzberg",
    "Win Nuding",
    "Andreas Klümper",
    "Ara Sedrakyan"
  ],
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.mes-hall",
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "In this paper we propose a new $S$-matrix approach to numerical simulations of network models and apply it to random networks that we proposed in a previous work 10.1103/PhysRevB.95.125414. Random networks are modifications of the Chalker-Coddington (CC) model for the integer quantum Hall transition that more faithfully capture the physics of electrons moving in a strong magnetic field and a smooth disorder potential. The new method has considerable advantages compared to the transfer matrix approach, and gives the value $\\nu \\approx 2.4$ for the critical exponent of the localization length in a random network. This finding confirms our previous result and is surprisingly close to the experimental value $\\nu_{\\text{exp}} \\approx 2.38$ observed at the integer quantum Hall transition but substantially different from the CC value $\\nu_\\text{CC} \\approx 2.6$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-04T19:35:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integer quantum hall transition",
      "random network",
      "transfer matrix approach",
      "strong magnetic field",
      "smooth disorder potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}