Double occupancies in confined attractive fermions on optical lattices

TL;DR

This paper investigates the phase behavior of confined attractive fermions in optical lattices using numerical methods, focusing on double occupancy and local density to identify composite phases.

Contribution

It introduces a numerical approach combining the Bethe-ansatz solution with the Thomas-Fermi approximation to analyze phase diagrams and local properties in a 1D fermion Hubbard model.

Findings

Phase diagram of attractive fermions mapped out.

Double occupancy and local density effectively detect composite phases.

Identification of phase transitions induced by trapping potential.

Abstract

We perform a numerical study of a one-dimensional Fermion-Hubbard model in harmonic traps within the Thomas-Fermi approximation based on the exact Bethe-ansatz solution. The $\rho-U/t$ phase diagram is shown for the systems of attractive interactions ($\rho$ is the characteristic density and $U/t$ the interaction strength scaled in units of the hopping parameter.). We study the double occupancy, the local central density and their derivatives. Their roles are discussed in details in detecting the composite phases induced by the trapping potential.