{
  "id": "1009.4646",
  "version": "v3",
  "published": "2010-09-23T15:54:20.000Z",
  "updated": "2010-12-21T15:39:52.000Z",
  "title": "Dynamical simulation of integrable and non-integrable models in the Heisenberg picture",
  "authors": [
    "Dominik Muth",
    "Razmik G. Unanyan",
    "Michael Fleischhauer"
  ],
  "comment": "4 pages, 2 figures",
  "journal": "Phys. Rev. Lett. 106, 077202 (2011)",
  "doi": "10.1103/PhysRevLett.106.077202",
  "categories": [
    "quant-ph",
    "cond-mat.other",
    "physics.comp-ph"
  ],
  "abstract": "The numerical simulation of quantum many-body dynamics is typically limited by the linear growth of entanglement with time. Recently numerical studies have shown, however, that for 1D Bethe-integrable models the simulation of local operators in the Heisenberg picture can be efficient as the corresponding operator-space entanglement grows only logarithmically. Using the spin-1/2 XX chain as generic example of an integrabel model that can be mapped to free particles, we here provide a simple explanation for this. We show furthermore that the same reduction of complexity applies to operators that have a high-temperature auto correlation function which decays slower than exponential, i.e., with a power law. This is amongst others the case for models where the Blombergen-De Gennes conjecture of high-temperature diffusive dynamics holds. Thus efficient simulability may already be implied by a single conservation law (like that of total magnetization), as we will illustrate numerically for the spin-1 XXZ model.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-12-21T15:39:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "75.10.Pq",
      "02.70.-c",
      "67.80.dk"
    ],
    "keywords": [
      "heisenberg picture",
      "dynamical simulation",
      "non-integrable models",
      "high-temperature auto correlation function",
      "high-temperature diffusive dynamics holds"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review Letters",
      "year": 2011,
      "month": "Feb",
      "volume": 106,
      "number": 7,
      "pages": "077202"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvL.106g7202M"
    }
  }
}