We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large- $N$ in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions of the two species can be tuned continuously as a function of the ratio. We also investigate the finite-size spectral properties of the model. We show how the level statistics differs from the original SYK model and infer an additional exchange symmetry in the bipartite model.We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large-$N$ in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions of the two species can be tuned continuously as a function of the ratio. We also investigate the finite-size spectral properties of the model. We show how the level statistics differs from the original SYK model and infer an additional exchange symmetry in the bipartite model.

arXiv:2111.15215Physical review. D/Physical review. D.Mar 28, 20226 citations

Imbalanced coupled Sachdev-Ye-Kitaev model

Sharmistha Sahoo, Rafael Haenel, Timothy H. Hsieh +1 more

Bulletin of the American Physical SocietyMar 18, 20210 citations

A bipartite Sachdev-Ye-Kitaev model: Conformal limit and finite size level statistics

Mikael Fremling, Masudul Haque, Lars Fritz

We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large-N in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions of the two species can be tuned continuously as a function of the ratio. We also investigate the finite size spectral properties of the model. We show how the level statistics differs from the original SYK model, and infer an additional exchange symmetry in the bipartite model.We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large-N in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions of the two species can be tuned continuously as a function of the ratio. We also investigate the finite size spectral properties of the model. We show how the level statistics differs from the original SYK model, and infer an additional exchange symmetry in the bipartite model.

Nov 30, 20210 citations

Invitation to the Sachdev-Ye-Kitaev Paradigm

Rishabh Jha

Lecture notes in physicsJan 1, 20260 citations

The Wishart-Sachdev-Ye-Kitaev model: Q-Laguerre spectral density and quantum chaos.

Lucas Sá, Antonio M. Garcı́a-Garcı́a

We study the Wishart-Sachdev-Ye-Kitaev (WSYK) model consisting of two $\hat{q}$ -body Sachdev-Ye-Kitaev (SYK) models with general complex couplings, one the complex conjugate of the other, living in off-diagonal blocks of a larger WSYK Hamiltonian. In the limit of large number $N$ of Majoranas and $\hat{q} \propto \sqrt N$ , we employ diagrammatic and combinatorial techniques to show that the spectral density of the model can be approximated by the weight function of the Al-Salam-Chihara Q-Laguerre polynomials. For $\hat{q} = 2, 3, 4$ , the analytical spectral density, with $Q=Q(\hat{q},N)$ computed analytically, agrees well with numerical results obtained by exact diagonalization. The spectrum is positive with a hard edge at zero energy and, for odd $\hat{q}$ , low-energy excitations grow as a stretched exponential, though the functional form is different from that of the supersymmetric SYK model. The microscopic spectral density and level statistics close to the hard edge are very well approximated by that of an ensemble of random matrices belonging to non-standard universality classes, which indicates quantum chaotic dynamics.We study the Wishart-Sachdev-Ye-Kitaev (WSYK) model consisting of two $\hat{q}$-body Sachdev-Ye-Kitaev (SYK) models with general complex couplings, one the complex conjugate of the other, living in off-diagonal blocks of a larger WSYK Hamiltonian. In the limit of large number $N$ of Majoranas and $\hat{q} \propto \sqrt N$, we employ diagrammatic and combinatorial techniques to show that the spectral density of the model can be approximated by the weight function of the Al-Salam-Chihara Q-Laguerre polynomials. For $\hat{q} = 2, 3, 4$, the analytical spectral density, with $Q=Q(\hat{q},N)$ computed analytically, agrees well with numerical results obtained by exact diagonalization. The spectrum is positive with a hard edge at zero energy and, for odd $\hat{q}$, low-energy excitations grow as a stretched exponential, though the functional form is different from that of the supersymmetric SYK model. The microscopic spectral density and level statistics close to the hard edge are very well approximated by that of an ensemble of random matrices belonging to non-standard universality classes, which indicates quantum chaotic dynamics.

Apr 15, 20211 citation

We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large-

N

in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions of the two species can be tuned continuously as a function of the ratio. We also investigate the finite-size spectral properties of the model. We show how the level statistics differs from the original SYK model and infer an additional exchange symmetry in the bipartite model.

We study the Wishart-Sachdev-Ye-Kitaev (WSYK) model consisting of two

\hat{q}

-body Sachdev-Ye-Kitaev (SYK) models with general complex couplings, one the complex conjugate of the other, living in off-diagonal blocks of a larger WSYK Hamiltonian. In the limit of large number

N

of Majoranas and

\hat{q} \propto \sqrt N

, we employ diagrammatic and combinatorial techniques to show that the spectral density of the model can be approximated by the weight function of the Al-Salam-Chihara Q-Laguerre polynomials. For

\hat{q} = 2, 3, 4

, the analytical spectral density, with

Q=Q(\hat{q},N)

computed analytically, agrees well with numerical results obtained by exact diagonalization. The spectrum is positive with a hard edge at zero energy and, for odd

\hat{q}

, low-energy excitations grow as a stretched exponential, though the functional form is different from that of the supersymmetric SYK model. The microscopic spectral density and level statistics close to the hard edge are very well approximated by that of an ensemble of random matrices belonging to non-standard universality classes, which indicates quantum chaotic dynamics.