{
  "id": "cond-mat/9810239",
  "version": "v1",
  "published": "1998-10-20T03:45:49.000Z",
  "updated": "1998-10-20T03:45:49.000Z",
  "title": "Universal Asymptotic Eigenvalue Distribution of Density Matrices and the Corner Transfer Matrices in the Thermodynamic Limit",
  "authors": [
    "Kouichi Okunishi",
    "Yasuhiro Hieida",
    "Yasuhiro Akutsu"
  ],
  "comment": "4 pages, RevTeX, 4 ps figures",
  "journal": "Phys. Rev. E 59 R6227 (1999)",
  "doi": "10.1103/PhysRevE.59.R6227",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the asymptotic behavior of the eigenvalue distribution of the Baxter's corner transfer matrix (CTM) and the density matrix (DM) in the White's density-matrix renormalization group (DMRG), for one-dimensional quantum and two-dimensional classical statistical systems. We utilize the relationship ${\\rm DM}={\\rm CTM}^4$ which holds for non-critical systems in the thermodynamic limit. Using the known diagonal form of CTM, we derive exact asymptotic form of the DM eigenvalue distribution for the integrable $S=1/2$ XXZ chain (and its related integrable models) in the massive regime. The result is then recast into a ``universal'' form without model-specific quantities, which leads to $\\omega_{m}\\sim \\exp[-{\\rm const.}(\\log m)^2]$ for $m$-th DM eigenvalue at larg $m$. We perform numerical renormalization group calculations (using the corner-transfer-matrix RG and the product-wavefunction RG) for non-integrable models, verifying the ``universal asymptotic form'' for them. Our results strongly suggest the universality of the asymptotic eigenvalue distribution of DM and CTM for a wide class of systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-10-20T03:45:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "universal asymptotic eigenvalue distribution",
      "corner transfer matrices",
      "thermodynamic limit",
      "density matrices",
      "numerical renormalization group calculations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "RevTeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}