{
  "id": "1601.02532",
  "version": "v1",
  "published": "2016-01-11T17:29:32.000Z",
  "updated": "2016-01-11T17:29:32.000Z",
  "title": "Cluster expansion for ground states of local Hamiltonians",
  "authors": [
    "Alvise Bastianello",
    "Spyros Sotiriadis"
  ],
  "comment": "49 pages, 24 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.quant-gas",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quench.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-11T17:29:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local hamiltonian",
      "cluster expansion",
      "ground state",
      "cluster amplitudes",
      "many-body quantum physics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160102532B",
      "inspire": 1414826
    }
  }
}