{
  "id": "2305.04984",
  "version": "v1",
  "published": "2023-05-08T18:29:38.000Z",
  "updated": "2023-05-08T18:29:38.000Z",
  "title": "Higher-Form Symmetry and Eigenstate Thermalization Hypothesis",
  "authors": [
    "Osamu Fukushima",
    "Ryusuke Hamazaki"
  ],
  "comment": "7 pages, 4 figures, supplemental material with 6 pages and 1 figure",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.str-el",
    "hep-th",
    "quant-ph"
  ],
  "abstract": "We elucidate how the presence of higher-form symmetries affects the dynamics of thermalization in isolated quantum systems. Under reasonable assumptions, we analytically show that a $p$-form symmetry in a $(d+1)$-dimensional quantum field theory leads to the breakdown of the eigenstate thermalization hypothesis for many nontrivial $(d-p)$-dimensional observables. For higher-form (i.e., $p\\geq 1$) symmetry, this indicates the absence of thermalization for observables that are non-local but much smaller than the whole system size. We numerically demonstrate this argument for the (2+1)-dimensional $\\mathbb{Z}_2$ lattice gauge theory. While local observables such as the plaquette operator thermalize, the non-local observable exciting a magnetic dipole instead relaxes to the generalized Gibbs ensemble that takes account of the $\\mathbb{Z}_2$ 1-form symmetry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-08T18:29:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eigenstate thermalization hypothesis",
      "higher-form symmetry",
      "dimensional quantum field theory",
      "higher-form symmetries affects",
      "lattice gauge theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}