{
  "annotation_id": "3c47bd7a-e11e-43da-98c5-463702e0fd0e",
  "date_created": "2026-03-02T18:01:45.463000Z",
  "date_modified": "2026-03-02T18:01:45.463000Z",
  "file_hash": "49cb8a2e75546d33297fd4cc5df3818d0bb1c4088e980883cd4c437ebbcc860a",
  "private": false,
  "record": {
    "abstract": "An elementary family of local Hamiltonians $H_{\\c ,\\ell}, \\ell = 1,2,3,\nldots$, is described for a $2-$dimensional quantum mechanical system of spin\n$={1/2}$ particles. On the torus, the ground state space $G_{\\circ,\\ell}$ is\n$(\\log)$ extensively degenerate but should collapse under $\\l$perturbation\" to\nan anyonic system with a complete mathematical description: the quantum double\nof the $SO(3)-$Chern-Simons modular functor at $q= e^{2 \\pi i/\\ell +2}$ which\nwe call $DE \\ell$. The Hamiltonian $H_{\\circ,\\ell}$ defines a\n\\underline{quantum} \\underline{loop}\\underline{gas}. We argue that for $\\ell =\n1$ and 2, $G_{\\circ,\\ell}$ is unstable and the collapse to $G_{\\epsilon, \\ell}\n\\cong DE\\ell$ can occur truly by perturbation. For $\\ell \\geq 3$,\n$G_{\\circ,\\ell}$ is stable and in this case finding $G_{\\epsilon,\\ell} \\cong DE\n\\ell$ must require either $\\epsilon \u003e \\epsilon_\\ell \u003e 0$, help from finite\nsystem size, surface roughening (see section 3), or some other trick, hence the\ninitial use of quotes ${\\l}\\quad$\". A hypothetical phase diagram is included in\nthe introduction.",
    "arxiv_id": "quant-ph/0110060",
    "authors": [
      "Michael H. Freedman"
    ],
    "categories": [
      "quant-ph",
      "cond-mat",
      "math.GT"
    ],
    "title": "A magnetic model with a possible Chern-Simons phase",
    "url": "https://arxiv.org/abs/quant-ph/0110060"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4394c181-daee-478c-ae00-73407edc7687",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}