{
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  "authors": [
    {
      "affiliations": [
        {
          "country": "USA", 
          "value": "School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, USA", 
          "organization": "Institute for Advanced Study"
        }
      ], 
      "surname": "Lashkari", 
      "email": "lashkari@ias.edu", 
      "full_name": "Lashkari, Nima", 
      "given_names": "Nima"
    }, 
    {
      "affiliations": [
        {
          "country": "USA", 
          "value": "Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA", 
          "organization": "Massachusetts Institute of Technology"
        }
      ], 
      "surname": "Liu", 
      "email": "hong_liu@mit.edu", 
      "full_name": "Liu, Hong", 
      "given_names": "Hong"
    }, 
    {
      "affiliations": [
        {
          "country": "USA", 
          "value": "Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA", 
          "organization": "Massachusetts Institute of Technology"
        }
      ], 
      "surname": "Rajagopal", 
      "email": "srivat91@mit.edu", 
      "full_name": "Rajagopal, Srivatsan", 
      "given_names": "Srivatsan"
    }
  ], 
  "titles": [
    {
      "source": "Springer", 
      "title": "Perturbation theory for the logarithm of a positive operator"
    }
  ], 
  "dois": [
    {
      "value": "10.1007/JHEP11(2023)097"
    }
  ], 
  "publication_info": [
    {
      "page_end": "24", 
      "journal_title": "Journal of High Energy Physics", 
      "material": "article", 
      "journal_volume": "2023", 
      "artid": "JHEP11(2023)097", 
      "year": 2023, 
      "page_start": "1", 
      "journal_issue": "11"
    }
  ], 
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    "source": "Springer", 
    "method": "Springer", 
    "submission_number": "89f97e94fe4811eeaf7a62370f8ccf13"
  }, 
  "page_nr": [
    24
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  "license": [
    {
      "url": "https://creativecommons.org/licenses//by/4.0", 
      "license": "CC-BY-4.0"
    }
  ], 
  "copyright": [
    {
      "holder": "The Author(s)", 
      "year": "2023"
    }
  ], 
  "control_number": "81436", 
  "record_creation_date": "2023-11-17T12:30:14.102292", 
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  "collections": [
    {
      "primary": "Journal of High Energy Physics"
    }
  ], 
  "arxiv_eprints": [
    {
      "categories": [
        "hep-th", 
        "math-ph", 
        "math.MP", 
        "quant-ph"
      ], 
      "value": "1811.05619"
    }
  ], 
  "abstracts": [
    {
      "source": "Springer", 
      "value": "In various contexts in mathematical physics, such as out-of-equilibrium physics and the asymptotic information theory of many-body quantum systems, one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the Tomita-Takesaki theory. Often, one encounters the situation where the operator under consideration, which we denote by \u2206, can be related by a perturbative series to another operator \u22060, whose logarithm is known. We set up a perturbation theory for the logarithm log \u2206. It turns out that the terms in the series possess a remarkable algebraic structure, which enables us to write them in the form of nested commutators plus some \u201ccontact terms\u201d."
    }
  ], 
  "imprints": [
    {
      "date": "2023-11-16", 
      "publisher": "Springer"
    }
  ]
}