Effective potential and quantum criticality for imbalanced Fermi mixtures

Area of Science:

• Condensed Matter Physics
• Quantum Phase Transitions
• Superfluidity

Background:

• Fermi mixtures exhibit complex phase diagrams near superfluid transitions.
• Understanding quantum critical points (QCPs) is crucial for low-temperature physics.
• Imbalanced Fermi gases offer a tunable platform to explore QCPs.

Purpose of the Study:

• To analyze the effective action for imbalanced Fermi superfluids at the superfluid onset.
• To investigate the possibility of suppressing the tricritical temperature to zero, enabling a quantum critical point.
• To determine the role of dimensionality (2D vs. 3D) in the existence of QCPs.

Main Methods:

• Analytical study of the effective action and Landau expansion.
• Mean-field theory calculations in 2D and 3D.
• Functional Renormalization Group (FRG) framework to study fluctuations beyond mean-field.

Main Results:

• In 3D, a quantum critical point is analytically identified at mean-field level.
• In 2D, a quantum critical point is excluded at mean-field level, except for specific parameter regimes.
• The Landau expansion is well-defined in the limit [Formula: see text] for most parameters.
• The stability of the 3D quantum critical point is confirmed beyond mean-field using FRG.

Conclusions:

• Dimensionality plays a critical role in the existence of quantum critical points in imbalanced Fermi superfluids.
• A stable quantum critical point is achievable in 3D, offering new avenues for exploring quantum criticality.
• The findings provide a theoretical foundation for experimental investigations of quantum phase transitions in ultracold Fermi gases.