Sachdev-Ye-Kitaev Model with Quadratic Perturbations: The Route to a Non-Fermi Liquid.

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• High-Energy Physics

Background:

• The Sachdev-Ye-Kitaev (SYK) model describes strongly correlated quantum systems.
• Understanding the stability of SYK models is crucial for their applications.
• The SYK_{4} model exhibits specific infrared asymptotic behavior.

Purpose of the Study:

• To investigate the stability of the Sachdev-Ye-Kitaev (SYK_{4}) model under a quadratic fermionic perturbation.
• To analyze the impact of the SYK_{2} perturbation on the SYK_{4} model's infrared properties.
• To explore the potential for developing theories of non-Fermi-liquid states.

Main Methods:

• Development of analytic perturbation theory for the SYK_{2} perturbation amplitude.
• Analysis of the Green function's infrared asymptotic behavior (G(τ)∝1/τ^{3/2}).
• Confirmation through exact numerical diagonalization.

Main Results:

• Demonstrated stability of the SYK_{4} model's infrared asymptotic behavior under weak perturbation.
• Confirmed the characteristic Green function G(τ)∝1/τ^{3/2} remains robust.
• Perturbation theory in the SYK_{2} amplitude successfully analyzed stability.

Conclusions:

• The SYK_{4} model is stable against weak quadratic fermionic perturbations.
• The findings support the theoretical framework for non-Fermi-liquid states.
• This research paves the way for new theories of strongly interacting fermions.