Thermalization and chaos in a 1+1d QFT

Luca Delacrétaz (Kadanoff Center for Theoretical Physics and Enrico Fermi Institute, University of Chicago, Chicago, IL, 60637, USA) ; A. Fitzpatrick (Department of Physics, Boston University, Boston, MA, 02215, USA) ; Emanuel Katz (Department of Physics, Boston University, Boston, MA, 02215, USA) ; Matthew Walters (Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, CH-1015, Switzerland; Department of Theoretical Physics, Université de Genève, Genève, CH-1211, Switzerland)

We study aspects of chaos and thermodynamics at strong coupling in a scalar model using LCT numerical methods. We find that our eigenstate spectrum satisfies Wigner-Dyson statistics and that the coefficients describing eigenstates in our basis satisfy Random Matrix Theory (RMT) statistics. At weak coupling, though the bulk of states satisfy RMT statistics, we find several scar states as well. We then use these chaotic states to compute the equation of state of the model, obtaining results consistent with Conformal Field Theory (CFT) expectations at temperatures above the scale of relevant interactions. We also test the Eigenstate Thermalization Hypothesis by computing the expectation value of local operators in eigenstates, and check that their behavior is consistent with thermal CFT values at high temperatures. Finally, we compute the Spectral Form Factor (SFF), which has the expected behavior associated with the equation of state at short times and chaos at long times. We also propose a new technique for extracting the connected part of the SFF without the need of disorder averaging by using different symmetry sectors.

{
  "_oai": {
    "updated": "2023-07-11T00:33:28Z", 
    "id": "oai:repo.scoap3.org:75545", 
    "sets": [
      "JHEP"
    ]
  }, 
  "authors": [
    {
      "affiliations": [
        {
          "country": "USA", 
          "value": "Kadanoff Center for Theoretical Physics and Enrico Fermi Institute, University of Chicago, Chicago, IL, 60637, USA", 
          "organization": "University of Chicago"
        }
      ], 
      "surname": "Delacr\u00e9taz", 
      "email": "lvd@uchicago.edu", 
      "full_name": "Delacr\u00e9taz, Luca", 
      "given_names": "Luca"
    }, 
    {
      "affiliations": [
        {
          "country": "USA", 
          "value": "Department of Physics, Boston University, Boston, MA, 02215, USA", 
          "organization": "Boston University"
        }
      ], 
      "surname": "Fitzpatrick", 
      "email": "fitzpatr@bu.edu", 
      "full_name": "Fitzpatrick, A.", 
      "given_names": "A."
    }, 
    {
      "affiliations": [
        {
          "country": "USA", 
          "value": "Department of Physics, Boston University, Boston, MA, 02215, USA", 
          "organization": "Boston University"
        }
      ], 
      "surname": "Katz", 
      "email": "amikatz@bu.edu", 
      "full_name": "Katz, Emanuel", 
      "given_names": "Emanuel"
    }, 
    {
      "affiliations": [
        {
          "country": "Switzerland", 
          "value": "Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne, CH-1015, Switzerland", 
          "organization": "Institute of Physics, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL)"
        }, 
        {
          "country": "Switzerland", 
          "value": "Department of Theoretical Physics, Universit\u00e9 de Gen\u00e8ve, Gen\u00e8ve, CH-1211, Switzerland", 
          "organization": "Universit\u00e9 de Gen\u00e8ve"
        }
      ], 
      "surname": "Walters", 
      "email": "matthew.walters@epfl.ch", 
      "full_name": "Walters, Matthew", 
      "given_names": "Matthew"
    }
  ], 
  "titles": [
    {
      "source": "Springer", 
      "title": "Thermalization and chaos in a 1+1d QFT"
    }
  ], 
  "dois": [
    {
      "value": "10.1007/JHEP02(2023)045"
    }
  ], 
  "publication_info": [
    {
      "page_end": "31", 
      "journal_title": "Journal of High Energy Physics", 
      "material": "article", 
      "journal_volume": "2023", 
      "artid": "JHEP02(2023)045", 
      "year": 2023, 
      "page_start": "1", 
      "journal_issue": "2"
    }
  ], 
  "$schema": "http://repo.scoap3.org/schemas/hep.json", 
  "acquisition_source": {
    "date": "2023-07-11T00:31:12.883065", 
    "source": "Springer", 
    "method": "Springer", 
    "submission_number": "11d99a161f8211ee91ac6ee2827c7def"
  }, 
  "page_nr": [
    31
  ], 
  "license": [
    {
      "url": "https://creativecommons.org/licenses//by/4.0", 
      "license": "CC-BY-4.0"
    }
  ], 
  "copyright": [
    {
      "holder": "The Author(s)", 
      "year": "2023"
    }
  ], 
  "control_number": "75545", 
  "record_creation_date": "2023-02-06T03:30:18.010121", 
  "_files": [
    {
      "checksum": "md5:95901a0306da770d27958bc464d14da1", 
      "filetype": "xml", 
      "bucket": "5edc4efe-d053-433d-9177-a90fa231d034", 
      "version_id": "11c391e3-b305-43a8-bce5-69df4dbef39d", 
      "key": "10.1007/JHEP02(2023)045.xml", 
      "size": 14468
    }, 
    {
      "checksum": "md5:9abe64893ca2795e78c6a82a42398dea", 
      "filetype": "pdf/a", 
      "bucket": "5edc4efe-d053-433d-9177-a90fa231d034", 
      "version_id": "9222b8bf-46d0-49f7-b865-e32f5bfb838d", 
      "key": "10.1007/JHEP02(2023)045_a.pdf", 
      "size": 11322769
    }
  ], 
  "collections": [
    {
      "primary": "Journal of High Energy Physics"
    }
  ], 
  "arxiv_eprints": [
    {
      "categories": [
        "hep-th", 
        "cond-mat.stat-mech", 
        "cond-mat.str-el"
      ], 
      "value": "2207.11261"
    }
  ], 
  "abstracts": [
    {
      "source": "Springer", 
      "value": "We study aspects of chaos and thermodynamics at strong coupling in a scalar model using LCT numerical methods. We find that our eigenstate spectrum satisfies Wigner-Dyson statistics and that the coefficients describing eigenstates in our basis satisfy Random Matrix Theory (RMT) statistics. At weak coupling, though the bulk of states satisfy RMT statistics, we find several scar states as well. We then use these chaotic states to compute the equation of state of the model, obtaining results consistent with Conformal Field Theory (CFT) expectations at temperatures above the scale of relevant interactions. We also test the Eigenstate Thermalization Hypothesis by computing the expectation value of local operators in eigenstates, and check that their behavior is consistent with thermal CFT values at high temperatures. Finally, we compute the Spectral Form Factor (SFF), which has the expected behavior associated with the equation of state at short times and chaos at long times. We also propose a new technique for extracting the connected part of the SFF without the need of disorder averaging by using different symmetry sectors."
    }
  ], 
  "imprints": [
    {
      "date": "2023-02-03", 
      "publisher": "Springer"
    }
  ]
}
Published on:
03 February 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 2
Pages 1-31
DOI:
https://doi.org/10.1007/JHEP02(2023)045
arXiv:
2207.11261
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: