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

Year: 2026

Authors: Legramandi A., Bandyopadhyay S., Hauke P.

Autors Affiliation: Univ Trento, CNR INO, Pitaevskii BEC Ctr, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; Trento Inst Fundamental Phys & Applicat, INFN TIFPA, I-38123 Trento, Italy; Indian Inst Sci Educ & Res Thiruvananthapuram, Sch Phys, Thiruvananthapuram 695551, Kerala, India.

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.

Journal/Review: PHYSICAL REVIEW B

Volume: 113 (16)      Pages from: L161117-1  to: L161117-8

More Information: We thank Gopal Chandra Santra, David Pascual Solis, Neil Talwar, and Alex Windey for interesting discussions. This work was supported by the Swiss State Secretariat for Education, Research and lnnovation (SERI) under Contract No. UeMO19-5.1; the Ministry of University and Research through FARE grant for the project DAVNE (Grant R20PEX7Y3A) , and through project DYNAMITE QUANTERA2_00056, in the frame of ERANET COFUND QuantERA II-2021 call co-funded by the European Union (H2020, Grant Agreement No. 101017733) ; the European Union-Next Generation EU, Mission 4, Component 2-CUP E53D23002240006; and the Provincia Autonoma di Trento, and Q@TN, the joint laboratory between University of Trento, FBK-Fondazione Bruno Kessler, INFN-National Institute for Nuclear Physics, and CNR-National Research Council. S.B. acknowledges CINECA for the use of HPC resources under ISCRA-C projects ISSYK-2 (HP10CP8XXF) and DISYK (HP10CGNZG9) .
KeyWords: Quantum Simulator; Fluctuations; Localization; Statistics; State
DOI: 10.1103/49yw-h27c