Competition between Chaotic and Nonchaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• High Energy Physics

Background:

• The Sachdev-Ye-Kitaev (SYK) model is a key theoretical tool for exploring non-Fermi liquid properties, maximal chaos, and holographic duality.
• Understanding quantum phase transitions in solvable models provides crucial insights into complex many-body systems.

Purpose of the Study:

• To investigate a generalized SYK model with two coupled SYK systems of differing Majorana mode numbers.
• To identify and characterize quantum phase transitions and critical behaviors in this solvable model.

Main Methods:

• Analytical solution of a generalized SYK model with quadratic coupling between two SYK systems.
• Characterization of quantum phases using spectral functions, Lyapunov exponents, and entropy.
• Mapping the phase diagram across zero and finite temperatures.

Main Results:

• A zero-temperature quantum phase transition was discovered between two distinct non-Fermi liquid chaotic phases, driven by the ratio of mode numbers.
• A nonchaotic Fermi liquid phase exists at the critical point where mode numbers are equal.
• At finite temperatures, the Fermi liquid phase occupies a finite region, and a novel non-Fermi liquid phase emerges.

Conclusions:

• The generalized SYK model provides a concrete platform for studying transitions between non-Fermi liquid phases.
• The results demonstrate tunable quantum criticality and emergent phases in solvable interacting fermion systems.
• This work offers valuable insights into the complex phase diagrams of quantum chaotic systems.