{
  "id": "1910.11810",
  "version": "v1",
  "published": "2019-10-25T15:46:59.000Z",
  "updated": "2019-10-25T15:46:59.000Z",
  "title": "Existence of a spectral gap in the AKLT model on the hexagonal lattice",
  "authors": [
    "Marius Lemm",
    "Anders W. Sandvik",
    "Ling Wang"
  ],
  "comment": "12 pages; 8 figures",
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech",
    "cond-mat.str-el",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The $S=1$ AKLT quantum spin chain was the first rigorous example of an isotropic spin system in the Haldane phase. The conjecture that the $S=3/2$ AKLT model on the hexagonal lattice is also in a gapped phase has remained open, despite being a fundamental question of ongoing relevance to condensed-matter physics and quantum information theory. Here we confirm this conjecture by demonstrating the size-independent lower bound $\\Delta >0.006$ on the spectral gap of the hexagonal model with periodic boundary conditions in the thermodynamic limit. Our approach consists of two steps combining mathematical physics and high-precision computational physics. We first prove a mathematical finite-size criterion which gives a rigorous, size-independent bound on the spectral gap if the gap of a particular cut-out subsystem of 36 spins exceeds a certain threshold value. Then we verify the finite-size criterion by performing state-of-the-art DMRG calculations on the subsystem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-25T15:46:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral gap",
      "aklt model",
      "hexagonal lattice",
      "aklt quantum spin chain",
      "quantum information theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}