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

Johannes Dieplinger; Soumya Bera; Ferdinand Evers

doi:10.1016/j.aop.2021.168503

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arXiv · 2105.03208

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

Johannes Dieplinger·Soumya Bera·Ferdinand Evers

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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.

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Johannes Dieplinger, Soumya Bera, Ferdinand Evers. 2021-05-21. An SYK-inspired model with density-density interactions: spectral & wave function statistics, Green's function and phase diagram. https://doi.org/10.1016/j.aop.2021.168503

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