Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Theory

Background:

• The correlation energy of Fermi gases is crucial for understanding many-body quantum systems.
• Previous derivations of leading-order correlation energy were limited to small interaction potentials with compact Fourier support.

Purpose of the Study:

• To generalize the calculation of the leading order of the correlation energy for a Fermi gas.
• To extend the applicability to large interaction potentials, relaxing previous constraints.

Main Methods:

• The study employs approximate, collective bosonization in three dimensions.
• It involves deriving stronger bounds on non-bosonizable terms.
• Efficient control on the bosonization of the kinetic energy is also utilized.

Main Results:

• The leading order of the correlation energy for a Fermi gas has been derived for large interaction potentials.
• The generalization requires only a condition on the interaction potential's norm.
• Significant improvements in bounding non-bosonizable terms and controlling kinetic energy bosonization were achieved.

Conclusions:

• The findings extend the theoretical framework for calculating Fermi gas correlation energies.
• This work offers a more robust method applicable to a wider range of interaction potentials.
• The improved techniques pave the way for more accurate predictions in condensed matter systems.