{
  "id": "1907.04576",
  "version": "v1",
  "published": "2019-07-10T08:46:05.000Z",
  "updated": "2019-07-10T08:46:05.000Z",
  "title": "Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks",
  "authors": [
    "Laurens Vanderstraeten",
    "Bram Vanhecke",
    "Andreas M. Laeuchli",
    "Frank Verstraete"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "quant-ph"
  ],
  "abstract": "We apply variational tensor-network methods for simulating the Kosterlitz-Thouless phase transition in the classical two-dimensional XY model. In particular, using uniform matrix product states (MPS) with non-abelian O(2) symmetry, we compute the universal drop in the spin stiffness at the critical point. In the critical low-temperature regime, we focus on the MPS entanglement spectrum to characterize the Luttinger-liquid phase. In the high-temperature phase, we confirm the exponential divergence of the correlation length and estimate the critical temperature with high precision. Our MPS approach can be used to study generic two-dimensional phase transitions with continuous symmetries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-10T08:46:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical xy model",
      "tensor networks",
      "kosterlitz-thouless transition",
      "study generic two-dimensional phase transitions",
      "uniform matrix product states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}