Exact solution of a repulsive fermi model with enhanced superconducting correlations

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Theory
• Superconductivity

Background:

• Understanding emergent phenomena in interacting fermion systems is a key challenge.
• Investigating the role of interactions and their projection in exotic phases.
• Exploring mechanisms for superconductivity beyond conventional theories.

Purpose of the Study:

• To find the exact solution for a specific model of interacting fermions.
• To analyze the effects of pure repulsive interactions projecting onto a Cooper channel.
• To understand the emergence of superconducting enhancements and order.

Main Methods:

• Developed an exact solution based on the infinite-ranged nature of the interaction in real space.
• Utilized a functional integral approach dominated by a Gaussian term.
• Applied the 'order by projection' concept to analyze emergent properties.

Main Results:

• Achieved an exact solution for the fermion model in any dimension.
• Demonstrated strong superconducting enhancements due to the repulsive interaction.
• Observed quasi-long-ranged order in a Cooper channel not explicitly in the Hamiltonian.

Conclusions:

• The 'order by projection' mechanism can induce superconductivity and quasi-long-ranged order.
• Infinite-ranged interactions simplify the model, enabling an exact analytical solution.
• This work provides a new perspective on achieving superconductivity through repulsive forces.