{
  "annotation_id": "c368da21-e093-4cd3-bad5-efcd988901f0",
  "date_created": "2026-03-02T18:02:33.642000Z",
  "date_modified": "2026-03-02T18:02:33.642000Z",
  "file_hash": "e1d0b1ae8d52c9f5ea8836fe4be520ac397fe309353c62f2e1c46712954ad5d2",
  "private": false,
  "record": {
    "abstract": "We consider a one-parameter family of matrix product states of spin one\nparticles on a periodic chain and study in detail the entanglement properties\nof such a state. In particular we calculate exactly the entanglement of one\nsite with the rest of the chain, and the entanglement of two distant sites with\neach other and show that the derivative of both these properties diverge when\nthe parameter $g$ of the states passes through a critical point. Such a point\ncan be called a point of quantum phase transition, since at this point, the\ncharacter of the matrix product state which is the ground state of a\nHamiltonian, changes discontinuously. We also study the finite size effects and\nshow how the entanglement depends on the size of the chain. This later part is\nrelevant to the field of quantum computation where the problem of initial state\npreparation in finite arrays of qubits or qutrits is important. It is also\nshown that entanglement of two sites have scaling behavior near the critical\npoint.",
    "arxiv_id": "quant-ph/0702036",
    "authors": [
      "S. Alipour",
      "V. Karimipour",
      "L. Memarzadeh"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.75.052322",
    "journal_ref": "Phys. Rev. A 75, 052322 (2007)",
    "title": "Entanglement and quantum phase transitions in matrix product spin one   chains",
    "url": "https://arxiv.org/abs/quant-ph/0702036"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "60b2ef42-d60e-44ff-97f4-003fd9773640",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}