{
  "id": "2007.02959",
  "version": "v1",
  "published": "2020-07-06T18:00:04.000Z",
  "updated": "2020-07-06T18:00:04.000Z",
  "title": "Numerical evidence for many-body localization in two and three dimensions",
  "authors": [
    "Eli Chertkov",
    "Benjamin Villalonga",
    "Bryan K. Clark"
  ],
  "comment": "main paper: 8 pages, 4 figures; supplement: 21 pages, 19 figures",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "Disorder and interactions can lead to the breakdown of statistical mechanics in certain quantum systems, a phenomenon known as many-body localization (MBL). Much of the phenomenology of MBL emerges from the existence of localized-bits, or $\\ell$-bits, a set of conserved quantities that are spatially localized and binary (i.e., possess only $\\pm 1$ eigenvalues). While MBL and $\\ell$-bits are known to exist in one-dimensional systems, their existence in dimensions greater than one is a key open question. To tackle this question, we develop an algorithm that can find approximate binary $\\ell$-bits in arbitrary dimensions by adaptively generating a basis of operators in which to represent the $\\ell$-bit. We use the algorithm to study four models: the one-, two-, and three-dimensional disordered Heisenberg models and the two-dimensional disordered hard-core Bose-Hubbard model. For all four of the models studied, our algorithm finds high-quality $\\ell$-bits at large disorder strength and rapid qualitative changes in the distributions of $\\ell$-bits in particular ranges of disorder strengths, suggesting the existence of MBL transitions. These transitions in the one-dimensional Heisenberg model and two-dimensional Bose-Hubbard model coincide well with past estimates of the critical disorder strengths in these models which further validates the evidence of MBL-like behavior in the other two and three-dimensional models we examine. In addition to finding MBL-like behavior in higher dimensions, our algorithm can be used to probe MBL in various geometries and dimensionality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-06T18:00:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "many-body localization",
      "dimensions",
      "numerical evidence",
      "disorder strength",
      "two-dimensional bose-hubbard model coincide"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}