{
  "id": "2412.17600",
  "version": "v1",
  "published": "2024-12-23T14:19:44.000Z",
  "updated": "2024-12-23T14:19:44.000Z",
  "title": "The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group",
  "authors": [
    "Vincent Lahoche",
    "Dine Ousmane Samary",
    "Parham Radpay"
  ],
  "comment": "74 pages, 32 figures",
  "categories": [
    "cond-mat.dis-nn",
    "hep-th"
  ],
  "abstract": "To gain a deeper understanding of the glassy phase in $p$-spin quantum models, this paper examines the dynamics of the $N$-vector $\\bm{x} \\in \\mathbb{R}^N$ through the framework of renormalization group theory. First, we focus on perturbation theory, which is more suitable than nonperturbative techniques due to the specific temporal non-locality of the model after disorder integration. We compute the one-loop $\\beta$-function and explore the structure of its fixed points. Next, we develop the nonperturbative renormalization group approach based on the standard Wetterich-Morris formalism, using two approximation schemes to address the model's non-locality. We investigate the vertex expansion in the symmetric phase and assess the reliability of the approximations for the fixed-point solutions. Finally, we extend our analysis beyond the symmetric phase by using an expansion around the vacuum of the local potential. Our numerical investigations particularly focus on the cases $p = 2$ and $p=3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-23T14:19:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional renormalization group",
      "spin renormalization group",
      "symmetric phase",
      "standard wetterich-morris formalism",
      "spin quantum models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 74,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}