Symmetry classes, many-body zero modes, and supersymmetry in the complex Sachdev-Ye-Kitaev model

• DOI: 10.1103/physrevd.101.066017
• Publication Date: 2020-03-20T20:14:30Z
• Authors: Jan Behrends; Benjamin Béri
• Keywords: Fermion doubling; Parity (physics)

The complex Sachdev-Ye-Kitaev (cSYK) model is a charge-conserving of randomly interacting fermions. interaction term can be chosen such that the exhibits chiral symmetry. Then, depending on charge sector and number fermions, level spacing statistics suggests fourfold categorization into three Wigner-Dyson symmetry classes. In this work, inspired by previous findings for Majorana model, we embed classes cSYK in Altland-Zirnbauer framework identify consequences originating from correlations across different sectors. particular, show an odd hosts exact many-body zero modes combined generalized fermion does not affect system's energy. This directly leads to quantum-mechanical supersymmetry that, unlike explicitly supersymmetric constructions, require fine-tuned couplings, but only Signatures fermion, thus supersymmetry, include long-time plateau time-dependent correlation functions fermion-parity-odd observables: may take nonzero value certain combinations structure observable class. We illustrate our through diagonalization simulations dynamics.