{
  "id": "1608.02205",
  "version": "v1",
  "published": "2016-08-07T11:41:05.000Z",
  "updated": "2016-08-07T11:41:05.000Z",
  "title": "Analytic Optimization of a MERA network and its Relevance to Quantum Integrability and Wavelet",
  "authors": [
    "Hiroaki Matsueda"
  ],
  "comment": "18 pages, 3 figures",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "I present an example of how to analytically optimize a multiscale entanglement renormalization ansatz for a finite antiferromagnetic Heisenberg chain. For this purpose, a quantum-circuit representation is taken into account, and we construct the exactly entangled ground state so that a trivial IR state is modified sequentially by operating separated entangler layers (monodromy operators) at each scale. The circuit representation allows us to make a simple understanding of close relationship between the entanglement renormalization and quantum integrability. We find that the entangler should match with the $R$-matrix, not a simple unitary, and also find that the optimization leads to the mapping between the Bethe roots and the Daubechies wavelet coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-07T11:41:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum integrability",
      "analytic optimization",
      "mera network",
      "multiscale entanglement renormalization ansatz",
      "finite antiferromagnetic heisenberg chain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}