A bstract It is known that, for a range of chemical potentials, the infrared behavior of the complex Sachdev-Ye-Kitaev (cSYK) model is governed by a 1D Nearly Conformal Field Theory (NCFT 1 ), thereby realizing a continuous line of NCFTs. A finite chemical potential μ introduces an asymmetry parameter $\mathcal{E}$ E into the cSYK fermion two-point function in the conformal limit. In this work, we compute the cSYK four-point function in the conformal limit for an arbitrary value of $\mathcal{E}$ E at leading order in 1/ N . We show that the result is fully consistent with the NCFT 1 structure of the cSYK model and use it to extract the structure constants for correlation functions of two complex fermions with bilinear operators.A bstract It is known that, for a range of chemical potentials, the infrared behavior of the complex Sachdev-Ye-Kitaev (cSYK) model is governed by a 1D Nearly Conformal Field Theory (NCFT 1 ), thereby realizing a continuous line of NCFTs. A finite chemical potential μ introduces an asymmetry parameter $$ \mathcal{E} $$ E into the cSYK fermion two-point function in the conformal limit. In this work, we compute the cSYK four-point function in the conformal limit for an arbitrary value of $$ \mathcal{E} $$ E at leading order in 1/ N . We show that the result is fully consistent with the NCFT 1 structure of the cSYK model and use it to extract the structure constants for correlation functions of two complex fermions with bilinear operators.

arXiv:2601.04330Journal of High Energy PhysicsSep 2, 20260 citations

Approximation of the Sachev-Ye-Kitaev Model by Free Fermion Variational States

Daniel Ish, Mark Srednicki

Bulletin of the American Physical SocietyMar 6, 20180 citations

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

Jan Behrends, Benjámin Béri

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.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.

arXiv:1912.09975Physical review. D/Physical review. D.Mar 20, 20207 citations

Towards quantum simulation of Sachdev-Ye-Kitaev model

Ye Cao, Yi-Neng Zhou, Ting-Ting Shi +1 more

arXiv:2003.01514中国科学通报：英文版Mar 27, 20206 citations

Large q expansion in the Sachdev-Ye-Kitaev model

Grigory Tarnopolsky

We consider the Sachdev-Ye-Kitaev (SYK) model, where interaction involves $q$ fermions at a time. We find the $1/{q}^{2}$ correction to the thermal two-point function in the large $q$ expansion. Using this result, we find the $1/{q}^{3}$ correction to the SYK free energy.We consider the Sachdev-Ye-Kitaev (SYK) model, where interaction involves $q$ fermions at a time. We find the $1/{q}^{2}$ correction to the thermal two-point function in the large $q$ expansion. Using this result, we find the $1/{q}^{3}$ correction to the SYK free energy.

arXiv:1801.06871Physical review. D/Physical review. D.Jan 15, 201933 citations

\mathcal{E}

E into the cSYK fermion two-point function in the conformal limit. In this work, we compute the cSYK four-point function in the conformal limit for an arbitrary value of

\mathcal{E}

E at leading order in 1/ N . We show that the result is fully consistent with the NCFT 1 structure of the cSYK model and use it to extract the structure constants for correlation functions of two complex fermions with bilinear operators.

We consider the Sachdev-Ye-Kitaev (SYK) model, where interaction involves

q

fermions at a time. We find the

1/{q}^{2}

correction to the thermal two-point function in the large

q

expansion. Using this result, we find the

1/{q}^{3}

correction to the SYK free energy.