{
  "id": "0807.0972",
  "version": "v1",
  "published": "2008-07-07T09:14:59.000Z",
  "updated": "2008-07-07T09:14:59.000Z",
  "title": "Canonical representation for electrons and its application to the Hubbard model",
  "authors": [
    "Brijesh Kumar"
  ],
  "comment": "10+ pages, 3 Figures",
  "journal": "Phys. Rev. B 77, 205115 (2008)",
  "doi": "10.1103/PhysRevB.77.205115",
  "categories": [
    "cond-mat.str-el"
  ],
  "abstract": "A new representation for electrons is introduced, in which the electron operators are written in terms of a spinless fermion and the Pauli operators. This representation is canonical, invertible and constraint-free. Importantly, it simplifies the Hubbard interaction. On a bipartite lattice, the Hubbard model is reduced to a form in which the exchange interaction emerges simply by decoupling the Pauli subsystem from the spinless fermion bath. This exchange correctly reproduces the large $U$ superexchange. Also derived, for $U=\\pm\\infty$, is the Hamiltonian to study Nagaoka ferromagnetism. In this representation, the infinite-$U$ Hubbard problem becomes elegant and easier to handle. Interestingly, the ferromagnetism in Hubbard model is found to be related to the gauge invariance of the spinless fermions. Generalization of this representation for the multicomponent fermions, a new representation for bosons, the notion of a `soft-core' fermion, and some interesting unitary transformations are introduced and discussed in the appendices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-07T09:14:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "71.10.Fd",
      "75.10.Jm",
      "05.30.Fk"
    ],
    "keywords": [
      "hubbard model",
      "canonical representation",
      "application",
      "study nagaoka ferromagnetism",
      "exchange interaction emerges"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review B",
      "year": 2008,
      "month": "May",
      "volume": 77,
      "number": 20,
      "pages": 205115
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvB..77t5115K"
    }
  }
}