{
  "id": "2005.01758",
  "version": "v1",
  "published": "2020-05-04T18:01:47.000Z",
  "updated": "2020-05-04T18:01:47.000Z",
  "title": "Prime Suspects in a Quantum Ladder",
  "authors": [
    "Giuseppe Mussardo",
    "Andrea Trombettoni",
    "Zhao Zhang"
  ],
  "comment": "5 pages, 2 figures + Supplementary Material",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we set up a suggestive number theory interpretation of a quantum ladder system made of ${\\mathcal N}$ coupled chains of spin 1/2. Using the hard-core boson representation, we associate to the spins $\\sigma_a$ along the chains the prime numbers $p_a$ so that the chains become quantum registers for square-free integers. The Hamiltonian of the system consists of a hopping term and a magnetic field along the chains, together with a repulsion rung interaction and a permutation term between next neighborhood chains . The system has various phases, among which there is one whose ground state is a coherent superposition of the first ${\\mathcal N}$ prime numbers. We also discuss the realization of such a model in terms of an open quantum system with a dissipative Lindblad dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-04T18:01:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "prime suspects",
      "prime numbers",
      "quantum ladder system",
      "hard-core boson representation",
      "suggestive number theory interpretation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}