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

TL;DR

This paper introduces a variant of the SYK model with density-density interactions that restores integrability, revealing multiple phases including a chaotic phase with SYK-like properties, bridging the gap to more realistic systems.

Contribution

It proposes a new SYK-inspired model with density-density interactions that exhibits multiple phases, including a chaotic phase with SYK signatures, enhancing the model's physical relevance.

Findings

The model shows two integrable phases separated by intermediate phases.

The chaotic phase exhibits spectral and Green's function signatures similar to the original SYK model.

Numerical results suggest the chaotic phase is connected to the non-Fermi liquid phase of SYK.

Abstract

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.