An SYK-inspired model with density-density interactions: Spectral & wave function statistics, Green's function and phase diagram

The Sachdev-Ye-Kitaev (SYK) model is a rare example of a strongly-interacting system that is analytically tractable. Tractability arises because the model is largely structureless by design and therefore artificial: while the interaction is restricted to two-body terms, interaction matrix elements are randomized and therefore the corresponding interaction operator does not commute with the local density. Unlike conventional density-density-type interactions, the SYK-interaction is, in this sense, not integrable. We here investigate a variant of the (complex) SYK model, which restores this integrability. It features a randomized single-body term and a density-density-type interaction. We present numerical investigations suggesting that the model exhibits two integrable phases separated by several intermediate phases including a chaotic one. The chaotic phase carries several characteristic SYK-signatures including in the spectral statistics and the frequency scaling of the Green's function and therefore should be adiabatically connected to the non-Fermi liquid phase of the original SYK model. Thus, our model Hamiltonian provides a bridge from the SYK-model towards microscopic realism. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The Sachdev-Ye-Kitaev (SYK) model is a rare example of a strongly-interacting system that is analytically tractable due to its largely structureless design. By investigating a variant of the complex SYK model, it was found to exhibit two integrable phases and several intermediate phases, including a chaotic one, which shows characteristic SYK-signatures. The chaotic phase is believed to be adiabatically connected to the non-Fermi liquid phase of the original SYK model, indicating a bridge from the SYK model towards microscopic realism.