Abstract
The complex Sachdev-Ye-Kitaev (cSYK) model is a charge-conserving model of randomly interacting fermions. The interaction term can be chosen such that the model exhibits chiral symmetry. Then, depending on the charge sector and the number of interacting fermions, level spacing statistics suggests a fourfold categorization of the model into the three Wigner-Dyson symmetry classes. In this work, inspired by previous findings for the Majorana Sachdev-Ye-Kitaev model, we embed the symmetry classes of the cSYK model in the Altland-Zirnbauer framework and identify consequences of chiral symmetry originating from correlations across different charge sectors. In particular, we show that for an odd number of fermions, the model hosts exact many-body zero modes that can be combined into a generalized fermion that does not affect the system's energy. This fermion directly leads to quantum-mechanical supersymmetry that, unlike explicitly supersymmetric cSYK constructions, does not require fine-tuned couplings, but only chiral symmetry. Signatures of the generalized fermion, and thus supersymmetry, include the long-time plateau in time-dependent correlation functions of fermion-parity-odd observables: The plateau may take nonzero value only for certain combinations of the fermion structure of the observable and the system's symmetry class. We illustrate our findings through exact diagonalization simulations of the system's dynamics.
Highlights
The holographic principle is a conjectured relationship between gravitational and lower-dimensional conformal field theories [1,2,3,4]
We show that the many-body zero modes of the oddN, chiral-symmetric, complex Sachdev-Ye-Kitaev (cSYK) model can be combined into a generalized fermion and that the presence of this means that the system is supersymmetric
In this work we have embedded the fourfold pattern of level spacing statistics [35] for the chiral-symmetric complex-fermion SYK model into the Altland-Zirnbauer symmetry classification first introduced for its Majorana counterpart [37]
Summary
The holographic principle is a conjectured relationship between gravitational and lower-dimensional conformal field theories [1,2,3,4]. This eightfold pattern was later understood to originate from a symmetry classification beyond Wigner-Dyson, namely the realization of the eight real Altland-Zirnbauer classes [36] in the SYK model [37] This has several structural consequences, including many-body zero modes [37] and quantum mechanical supersymmetry [38], and signatures beyond level spacing statistics, in particular in fermion-parity-odd correlation functions [37,38,39]. For the cSYK model with chiral symmetry, You et al found that the number N of complex fermions and the charge quantum number q together determine a fourfold pattern for the three Wigner-Dyson level spacing statistics This leads us to the main questions of this work: Is there a symmetry classification beyond Wigner-Dyson behind this fourfold pattern and, if so, what are its structural consequences and signatures?. VI and give an outlook on possible extensions of our results
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