{
  "id": "cond-mat/0601237",
  "version": "v3",
  "published": "2006-01-11T18:51:07.000Z",
  "updated": "2006-05-17T01:44:04.000Z",
  "title": "Entanglement entropy and the Berry phase in solid states",
  "authors": [
    "S. Ryu",
    "Y. Hatsugai"
  ],
  "comment": "11 pages, 4 figures, new references added",
  "journal": "Phys. Rev. B 73, 245115 (2006)",
  "doi": "10.1103/PhysRevB.73.245115",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.str-el",
    "quant-ph"
  ],
  "abstract": "The entanglement entropy (von Neumann entropy) has been used to characterize the complexity of many-body ground states in strongly correlated systems. In this paper, we try to establish a connection between the lower bound of the von Neumann entropy and the Berry phase defined for quantum ground states. As an example, a family of translational invariant lattice free fermion systems with two bands separated by a finite gap is investigated. We argue that, for one dimensional (1D) cases, when the Berry phase (Zak's phase) of the occupied band is equal to $\\pi \\times ({odd integer})$ and when the ground state respects a discrete unitary particle-hole symmetry (chiral symmetry), the entanglement entropy in the thermodynamic limit is at least larger than $\\ln 2$ (per boundary), i.e., the entanglement entropy that corresponds to a maximally entangled pair of two qubits. We also discuss this lower bound is related to vanishing of the expectation value of a certain non-local operator which creates a kink in 1D systems.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-05-17T01:44:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "entanglement entropy",
      "berry phase",
      "solid states",
      "ground state",
      "von neumann entropy"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. B"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}