Perturbed Sachdev-Ye-Kitaev Model: A Polaron in the Hyperbolic Plane

Area of Science:

• Quantum mechanics
• Condensed matter physics
• High energy physics

Background:

• The Sachdev-Ye-Kitaev (SYK) model is a key theoretical framework for studying quantum chaos and black holes.
• Previous studies primarily focused on the simplest perturbative limit of the SYK_{4} model.

Purpose of the Study:

• To investigate the behavior of the SYK_{4} model with a weak SYK_{2} perturbation beyond the perturbative limit.
• To determine the validity of the SYK_{4} mean-field solution under these conditions.
• To analyze the out-of-time-order correlation function (OTOC) and its temperature dependence.

Main Methods:

• Perturbative analysis of the SYK_{4} model with an added SYK_{2} term.
• Analysis of Schwarzian mode fluctuations.
• Calculation of the out-of-time-order correlation function.

Main Results:

• For intermediate perturbation strengths (J/N≪Γ≪J/sqrt[N]), Schwarzian mode fluctuations are suppressed.
• The SYK_{4} mean-field solution's validity is extended to longer timescales (t_{*}∼J/Γ^{2}).
• The OTOC exhibits exponential growth at short times with a maximal Lyapunov exponent of 2πT, and its prefactor scales as T at low temperatures (T≤Γ).

Conclusions:

• The weak SYK_{2} perturbation significantly alters the dynamics of the SYK_{4} model.
• The suppression of Schwarzian fluctuations leads to a more stable mean-field regime.
• The temperature scaling of the OTOC prefactor provides insights into quantum chaos at low temperatures.