Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models

Area of Science:

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

Background:

• Matrix quantum mechanics and Sachdev-Ye-Kitaev (SYK) models are crucial for understanding quantum chaos and black hole physics.
• Investigating these models at leading melonic order provides insights into their phase structure.

Purpose of the Study:

• To analyze the Schwinger-Dyson equations for fermionic planar matrix quantum mechanics, tensor, and SYK models.
• To identify and characterize distinct phases and phase transitions within these models.

Main Methods:

• Solving Schwinger-Dyson equations at leading melonic order.
• Analyzing fermionic and bosonic models, including unstable and stable variants.

Main Results:

• Identified two distinct phases: a high-entropy SYK black-hole-like phase and a low-entropy phase with trivial infrared behavior.
• Discovered a first-order phase transition line terminating at a novel critical point with non-mean-field critical exponents.
• Observed interesting phenomena in bosonic models, such as Kazakov critical points and inconsistencies in SYK-like infrared solutions.

Conclusions:

• The study reveals a rich phase structure in quantum mechanical models with implications for black hole physics.
• The critical behavior deviates from mean-field predictions, suggesting complex emergent dynamics.
• Further investigation into bosonic models is warranted due to observed inconsistencies.