{
  "id": "1702.03581",
  "version": "v1",
  "published": "2017-02-12T21:52:15.000Z",
  "updated": "2017-02-12T21:52:15.000Z",
  "title": "Entropy, gap and a multi-parameter deformation of the Fredkin spin chain",
  "authors": [
    "Zhao Zhang",
    "Israel Klich"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We introduce a general multi-parameter deformation of the Fredkin spin $1/2$ chain whose ground state is a weighted superposition of Dyck paths, depending on a set of parameters along the chain. The parameters are introduced in such a way to maintain the system frustration-free while allowing to explore a range of possible phases. In the case where the parameters are uniform, and when a color degree of freedom is added we establish a phase diagram with a transition between an area law and a volume low. The volume entropy obtained for half a chain is $n \\log (D/2)$ where $D$ is the dimension of the local spin Hilbert space, and $n$ is the half-chain length. We also prove an upper bound on the spectral gap, scaling as $\\Delta=O((2s)^nt^{-n^2/2})$, similar to a recent a result about the deformed Motzkin model, albeit derived in a different way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-12T21:52:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fredkin spin chain",
      "local spin hilbert space",
      "general multi-parameter deformation",
      "parameters",
      "spectral gap"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}