Skip to content
DraconiticResearch
Search Sources API
182,460 studies31 sourcesUpdated 13 min ago
PreprintCC BY 4.0arXiv

Airy distribution of the quenched spectral form factor in non-interacting fermions

  • Oscar Martin
  • Satya N. Majumdar
  • Laura Foini
Open at sourcePDFDOICite

Abstract

For chaotic many-body systems as well as the random energy model, the logarithm of the (scaled) spectral form factor (SFF) exhibits two robust properties at late times: (i) self-averaging and (ii) a reflected-Gumbel distribution. Here, we demonstrate that both properties break down for N non-interacting fermions on a lattice of size L with an incommensurate single-particle spectrum. We show that the logarithm of the SFF, upon rescaling by 1/√L, follows the Airy distribution, in stark contrast to the reflected-Gumbel law. Moreover, it is no longer self-averaging, as its mean and standard deviation are of the same order. While deviations from reflected-Gumbel statistics are generically expected for non-interacting systems, we find that an interacting integrable model exhibits reflected-Gumbel statistics at late times, mirroring the chaotic case and distinguishing it from non-interacting fermions.

Related

  1. Maximal Orbital Entanglement from Non-Interacting Fermions
    Damiano Aliverti-Piuri, Julia Liebert, Christian Schilling
    arXivPreprintCC BY 4.0Full textQuantum physics & quantum informationarXiv
  2. Strongly interacting fermions under imaginary rotation
    Tudor Pătuleanu, Victor E Ambruș
    HALPreprintarXiv licenceFull textHigh-energy & particle physicsNuclear physicsHALarXiv
  3. Symmetric mass generation of interacting chiral fermions on a one-dimensional lattice without fermion doubling
    V. A. Zakharov, Atsushi Ueda, Frank Verstraete +1
    arXivPreprintarXiv licenceFull textCondensed matterHigh-energy & particle physicsarXiv
  4. The quadratic density response function for non-interacting fermions at arbitrary temperature
    Pontus Svensson, Jan Vorberger, Zhandos A. Moldabekov +5
    arXivPreprintCC BY-SA 4.0Full textPlasma physicsarXiv
  5. New Developments in Diagrammatic Monte Carlo for Interacting Lattice Fermions: Efficient Algorithms and Applications
    Boyuan Shi
    arXivPreprintarXiv licenceFull textComputational physicsCondensed matterarXiv

Cite

BibTeXRIS
BibTeX
@misc{martin2026airy,
  title = {{Airy distribution of the quenched spectral form factor in non-interacting fermions}},
  author = {Oscar Martin and Satya N. Majumdar and Laura Foini},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41393},
  eprint = {2610.41393},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41393},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Airy distribution of the quenched spectral form factor in non-interacting fermions
AU  - Oscar Martin
AU  - Satya N. Majumdar
AU  - Laura Foini
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41393
UR  - https://arxiv.org/abs/2610.41393
AB  - For chaotic many-body systems as well as the random energy model, the logarithm of the (scaled) spectral form factor (SFF) exhibits two robust properties at late times: (i) self-averaging and (ii) a reflected-Gumbel distribution. Here, we demonstrate that both properties break down for N non-interacting fermions on a lattice of size L with an incommensurate single-particle spectrum. We show that the logarithm of the SFF, upon rescaling by 1/√L, follows the Airy distribution, in stark contrast to the reflected-Gumbel law. Moreover, it is no longer self-averaging, as its mean and standard deviation are of the same order. While deviations from reflected-Gumbel statistics are generically expected for non-interacting systems, we find that an interacting integrable model exhibits reflected-Gumbel statistics at late times, mirroring the chaotic case and distinguishing it from non-interacting fermions.
ER  -