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

Journal Article · Wed Dec 15 04:00:00 EST 2021 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2021.168503· OSTI ID:23183177

Dieplinger, Johannes ^[1]; Bera, Soumya ^[2]; Evers, Ferdinand ^[1]

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1. Institute of Theoretical Physics, University of Regensburg, D-93040 (Germany)
2. Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076 (India)

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.

• OSTI ID: 23183177
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 435; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DENSITY
FERMI GAS
HAMILTONIANS
MATRIX ELEMENTS
PHASE DIAGRAMS
WAVE FUNCTIONS