Ground state of the two-dimensional attractive Fermi gas: essential properties from few- to many-body

TL;DR

This study investigates the ground-state properties of two-dimensional attractive Fermi gases across few- to many-body systems using lattice Monte Carlo methods, revealing how properties evolve with particle number and interaction strength.

Contribution

It provides first-principles calculations of key properties for systems of 4 to 40 particles, elucidating the transition from few- to many-body behavior in 2D attractive Fermi gases.

Findings

Ground-state energy and Tan's contact determined across particle numbers and couplings.

Momentum distribution exhibits $k^{-4}$ tail with a shifting onset at different couplings.

Thermodynamic limit approached at lower N as attraction increases.

Abstract

We calculate the ground-state properties of unpolarized two-dimensional attractive fermions in the range from few to many particles. Using first-principles lattice Monte Carlo methods, we determine the ground-state energy, Tan's contact, momentum distribution, and single-particle correlation function. We investigate those properties for systems of $N=4,8,...,40$ particles and for a wide range of attractive couplings. As the attractive coupling is increased, the thermodynamic limit is reached at progressively lower $N$ due to the dominance of the two-body sector. At large momenta $k$, the momentum distribution displays the expected $k^{-4}$ behavior, but its onset shifts from $k \simeq 1.8 k^{}_F$ at weak coupling towards higher $k$ at strong coupling.