{
  "annotation_id": "0dea9b1d-d26c-4b1d-8da3-36b51fbeeb71",
  "date_created": "2026-03-02T18:02:07.041000Z",
  "date_modified": "2026-03-02T18:02:07.041000Z",
  "file_hash": "6ed731765c6c0a971760839e93dfede2efd435c013091f5dc3474a142103218a",
  "private": false,
  "record": {
    "abstract": "Motivated by its relation to an $\\cal{NP}$-hard problem, we analyze the\nground state properties of anti-ferromagnetic Ising-spin networks embedded on\nplanar cubic lattices, under the action of homogeneous transverse and\nlongitudinal magnetic fields. This model exhibits a quantum phase transition at\ncritical values of the magnetic field, which can be identified by the\nentanglement behavior, as well as by a Majorization analysis. The scaling of\nthe entanglement in the critical region is in agreement with the area law,\nindicating that even simple systems can support large amounts of quantum\ncorrelations. We study the scaling behavior of low-lying energy gaps for a\nrestricted set of geometries, and find that even in this simplified case, it is\nimpossible to predict the asymptotic behavior, with the data allowing equally\ngood fits to exponential and power law decays. We can therefore, draw no\nconclusion as to the algorithmic complexity of a quantum adiabatic ground-state\nsearch for the system.",
    "arxiv_id": "quant-ph/0401144",
    "authors": [
      "Cameron Wellard",
      "Roman Orus"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.str-el"
    ],
    "doi": "10.1103/PhysRevA.70.062318",
    "journal_ref": "Physical Review A 70, 062318 (2004)",
    "title": "Quantum Phase Transitions in Anti-ferromagnetic Planar Cubic Lattices",
    "url": "https://arxiv.org/abs/quant-ph/0401144"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1542ab32-5d0f-430c-b7f2-048422352a97",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}