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Updated: Dec 15, 2025

Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Periodic Table of the Ordinary and Supersymmetric Sachdev-Ye-Kitaev Models
1Department of Physics, Capital Normal University, Beijing 100048, China; Department of Physics and Astronomy, Mississippi State University, Mississippi State, Mississippi 39762, USA and Kavli Institute of Theoretical Physics, University of California, Santa Barbara, Santa Barbara, California 93106, USA.
Abstract:
We develop a unified minimal scheme to classify quantum chaos in the Sachdev-Ye-Kitaev (SYK) and supersymmetric (SUSY) SYK models and also work out the structure of the energy levels in one periodic table. The SYK with even q-body or SUSY SYK with odd q-body interaction, with N even or odd number of sites, are put on an equal footing in the minimal Hilbert space; N (mod 8), q (mod 4) double Bott periodicity, and a reflection condition are identified. Exact diagonalizations (EDs) are performed to study both the bulk energy level statistics and hard-edge behaviors. Excellent agreements between the ED results and the symmetry classifications are demonstrated. Our compact and systematic methods can be transformed to map out more complicated periodic tables of SYK models with more degrees of freedom, tensor models, or symmetry protected topological phases.
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