Solvable Strong-Coupling Quantum-Dot Model with a Non-Fermi-Liquid Pairing Transition.

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Statistical Mechanics

Background:

• Non-Fermi liquid behavior challenges conventional understanding of electron interactions in metals.
• Exotic pairing phenomena are crucial for understanding unconventional superconductivity.
• Quantum criticality describes phase transitions occurring at absolute zero temperature.

Purpose of the Study:

• To introduce and analyze the solvable random interacting Yukawa-SYK model.
• To investigate the emergence of non-Fermi-liquid and exotic pairing behaviors.
• To explore the conditions under which pairing is suppressed despite attractive interactions.

Main Methods:

• Development of a diagrammatic expansion controlled by 1/MN.
• Exact solution in the large-M, large-N limit.
• Solving the Eliashberg and renormalization group equations.

Main Results:

• The Yukawa-SYK model exhibits solvable non-Fermi-liquid behavior.
• Exotic pairing behavior is found, but only within a specific region of the (M,N) plane.
• Fermion incoherence can suppress Cooper pair formation, maintaining non-Fermi liquid states down to T=0.
• The transition to the pairing phase displays Kosterlitz-Thouless quantum-critical behavior.

Conclusions:

• The Yukawa-SYK model provides a tractable framework for studying complex quantum phenomena.
• Fermion incoherence plays a critical role in determining the presence or absence of pairing.
• The study reveals a quantum-critical transition into the pairing phase with unique characteristics.