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  • Letter
  • Open Access

Many-body spectral transitions through the lens of a variable-range quadratic Sachdev-Ye-Kitaev model

Andrea Legramandi*, Soumik Bandyopadhyay†,‡, and Philipp Hauke§

  • Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Universitá di Trento, Trento I38123, Italy and INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento 38123, Italy

  • *Contact author: andrea.legramandi@unitn.it
  • †Present address: School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Thiruvananthapuram, Kerala 695551, India.
  • ‡Contact author: soumik@iisertvm.ac.in
  • §Contact author: philipp.hauke@unitn.it
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Phys. Rev. B 113, L161117 – Published 21 April, 2026

DOI: https://doi.org/10.1103/49yw-h27c

Abstract

The Sachdev-Ye-Kitaev (SYK) model is a cornerstone in the study of quantum chaos and holographic quantum matter. Real-world implementations, however, deviate from the idealized all-to-all connectivity, raising questions about the robustness of its chaotic properties. In this work, we investigate a quadratic SYK model with distance-dependent interactions governed by a power-law decay. By analytically and numerically studying the spectral form factor (SFF), we uncover how transitions present in the single-particle limit carry over to the many-body system. Nontrivial cancellations in the one-loop contributions lead to a robustness of the SFF under a considerable reduction of the interaction range. Further suppression leads to a breakdown of perturbation theory around the infinite-range path-integral saddle and the appearance of spectral regimes, marked by a higher dip and the emergence of a secondary plateau. Our results highlight the interplay between single-particle criticality and many-body dynamics, offering insights into the quantum chaos-to-localization transition and its reflection in spectral statistics.

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Phys. Rev. B 113, L161117– Published 21 April, 2026
  • Received 12 February 2025
  • Revised 22 March 2026
  • Accepted 30 March 2026
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