{
  "id": "1812.03758",
  "version": "v1",
  "published": "2018-12-10T12:34:37.000Z",
  "updated": "2018-12-10T12:34:37.000Z",
  "title": "Quantum phase transitions in the spin-boson model without the counterrotating terms",
  "authors": [
    "Yan-Zhi Wang",
    "Shu He",
    "Liwei Duan",
    "Qing-Hu Chen"
  ],
  "comment": "8 pages, 6 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the spin-boson model without the counterrotating terms by a numerically exact method based on variational matrix product states. Surprisingly, the second-order quantum phase transition (QPT) is observed for the sub-Ohmic bath in the rotating-wave approximations. Moreover, the mean-field criticality is demonstrated for all bath exponents $0<s<1$, in contrast to the full spin-boson model. For large value of the bath exponent, a few first-order QPTs also appear before the critical points. With the decrease of the bath exponents, these first-order QPTs disappear successively, while the second-order QPT remains robust. The second-order QPT is further confirmed by multi-coherent-states variational studies, while the first-order QPT is corroborated with the exact diagonalization in the truncated Hilbert space. Extension to the Ohmic bath is also performed, and many first-order QPTs appear successively in a wide coupling regime. The previous picture for many physical phenomena based on the conserved total excitations in open quantum systems might be not valid at least for sub-ohmic baths at the strong coupling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-10T12:34:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "counterrotating terms",
      "first-order qpt",
      "bath exponent",
      "second-order qpt remains robust",
      "variational matrix product states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}