Many-body spectral transitions through the lens of the variable-range SYK2 model

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. Non-trivial 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 new 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 new insights into the quantum chaos-to-localization transition and its reflection in spectral statistics.

published version up to minor modifications

References in corpus (19)

• Anderson Transitions
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Phenomenology of fully many-body-localized systems
• Dipolar physics: A review of experiments with magnetic quantum gases
• Entanglement entropy for the long range Ising chain
• Many-Body Localization in the Age of Classical Computing
• Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
• Diverging equilibration times in long-range quantum spin models
• Can many-body localization persist in the presence of long-range interactions or long-range hopping?
• Measuring Spectral Form Factor in Many-Body Chaotic and Localized Phases of Quantum Processors
• Delayed Thermalization in Mass-Deformed SYK
• Scale-invariant critical dynamics at eigenstate transitions
• Entanglement Phases in large-N hybrid Brownian circuits with long-range couplings
• Fermionic quantum criticality and the fractal nodal surface
• Spectral statistics of a minimal quantum glass model
• Many-body Localization in Clean Chains with Long-Range Interactions
• Long-range spectral statistics of the Rosenzweig-Porter model
• Sparse random matrices and Gaussian ensembles with varying randomness
• Single-Particle Universality of the Many-Body Spectral Form Factor