Mott-Insulator Transition for Ultracold Fermions in Two-Dimensional Optical Lattices

TL;DR

This paper investigates the Mott-insulator transition of ultracold fermions in a 2D optical lattice using the Fermi-Hubbard model, analyzing phase diagrams, local phases, and effects of rotation, revealing connections to the Hofstadter butterfly.

Contribution

It introduces a mean-field analysis of the Mott-insulator transition in 2D optical lattices, including effects of harmonic trapping and rotation, linking phase boundaries to the Hofstadter butterfly.

Findings

Local Mott-insulator phases are centered in the trap with zero density variance.

Rotation influences the phase boundary, matching the Hofstadter butterfly edge.

Phase diagrams depend on trap and rotation parameters.

Abstract

In this work we study ultracold Fermions confined in a two-dimensional optical lattice and we explore the Mott-insulator transition with the Fermi-Hubbard model. On the basis of a mean-field approach, we study the phase diagrams in the presence of a harmonic trapping potential. Local Mott-insulator phases are shown to be generally situated in the center of the trap and correspond to a vanishing variance of the local density. We then study the effects induced by rotation on the Mott-insulator phase transition. In particular, we show that the phase boundary reproduces the edge of the Hofstadter butterfly.