Randomly Pruning the Sachdev-Ye-Kitaev Model

Research output: Contribution to journalArticlepeer-review

Abstract

The Sachdev-Ye-Kitaev model (SYK) is renowned for its short-time chaotic behavior, which plays a fundamental role in its application to various fields such as quantum gravity and holography. The Thouless energy, representing the energy scale at which the universal chaotic behavior in the energy spectrum ceases, can be determined from the spectrum itself. When simulating the SYK model on classical or quantum computers, it is advantageous to minimize the number of terms in the Hamiltonian by randomly pruning the couplings. In this paper, it is demonstrated that even with a significant pruning, eliminating a large number of couplings, the chaotic behavior persists up to short time scales. This is true even when only a fraction of the original (Formula presented.) couplings in the fully connected SYK model, specifically (Formula presented.), is retained. Here, L represents the number of sites, and (Formula presented.). The properties of the long-range energy scales, corresponding to short time scales, are verified through numerical singular value decomposition (SVD) and level number variance calculations.

Original languageEnglish
JournalAdvanced Quantum Technologies
DOIs
StateAccepted/In press - 2024

Keywords

  • Sachdev-Ye-Kitaev model
  • level statistics
  • quantum many body models
  • random matrix theory

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Electronic, Optical and Magnetic Materials
  • Nuclear and High Energy Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Theory and Mathematics
  • Electrical and Electronic Engineering

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