{
  "id": "quant-ph/0608057",
  "version": "v2",
  "published": "2006-08-07T11:25:41.000Z",
  "updated": "2006-09-14T11:45:05.000Z",
  "title": "Is efficiency of classical simulations of quantum dynamics related to integrability?",
  "authors": [
    "Tomaz Prosen",
    "Marko Znidaric"
  ],
  "comment": "4 pages; v2. added paragraph discussing pure states",
  "journal": "Phys.Rev.E 75, 015202 (2007)",
  "doi": "10.1103/PhysRevE.75.015202",
  "categories": [
    "quant-ph",
    "cond-mat.other",
    "nlin.SI"
  ],
  "abstract": "Efficiency of time-evolution of quantum observables, and thermal states of quenched hamiltonians, is studied using time-dependent density matrix renormalization group method in a family of generic quantum spin chains which undergo a transition from integrable to non-integrable - quantum chaotic case as control parameters are varied. Quantum states (observables) are represented in terms of matrix-product-operators with rank D_\\epsilon(t), such that evolution of a long chain is accurate within fidelity error \\epsilon up to time t. We find that rank generally increases exponentially, D_\\epsilon(t) \\propto \\exp(const t), unless the system is integrable in which case we find polynomial increase.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-09-14T11:45:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum dynamics",
      "classical simulations",
      "density matrix renormalization group method",
      "efficiency",
      "time-dependent density matrix renormalization group"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}