Dipolar extended Fermi-Hubbard Model in two-dimensions*

The ability to cool bosonic and fermionic atoms down to ultra cold temperatures in optical lattices has enabled the experimental emulation of model Hamiltonians for strongly correlated systems. Unlike in Condensed Matter systems, one has control over the model parameters such as interaction strength, hopping amplitude, and population imbalance. A recent experimental development in cold gases is the ability to create quantum degenerate bosonic and fermionic gases of magnetic atoms, leading to the study of magnetic dipolar interactions. The extended Bose-Hubbard model was recently emulated with ¹⁶⁸Er atoms in an optical lattice. The study of fermionic systems with anisotropic interactions beyond on-site is clearly in order. Here we use the Lanczos method to explore the ground state phase diagram of the dipolar extended Fermi-Hubbard Model at half-filling and two-dimensions. The anisotropic character of the dipole-dipole interaction, nearest-neighbour as well as next-nearest-neighbour interactions are taken into account. We observe quantum phase transitions between Antiferromagnetic and different Charge-Density Waves phases.