Phase Diagram of the Half-Filled Extended Hubbard Model in Two Dimensions

TL;DR

This paper maps the zero-temperature phase diagram of a two-dimensional extended Hubbard model with various interactions, revealing the stability regions of charge, spin, orbital, and nematic orders depending on hopping parameters.

Contribution

It provides the first detailed Hartree-Fock phase diagram including orbital antiferromagnetism and spin nematic states in the extended Hubbard model.

Findings

Orbital antiferromagnetism is stable at non-zero t' values.

Charge and spin density waves dominate at t' = 0.

Stability regions of exotic orders grow with increasing t'.

Abstract

We consider an extended Hubbard model of interacting fermions on a lattice. The fermion kinetic energy corresponds to a tight binding Hamiltonian with nearest neighbour (-t) and next nearest neighbour (t') hopping matrix elements. In addition to the onsite Hubbard interaction (U) we also consider a nearest neighbour repulsion (V). We obtain the zero temperature phase diagram of our model within the Hartree-Fock approximation. We consider ground states having charge and spin density wave ordering as well as states with orbital antiferromagnetism or spin nematic order. The latter two states correspond to particle-hole binding with $d_{x^2-y^2}$ symmetry in the charge and spin channels respectively. For $t' = 0$, only the charge density wave and spin density wave states are energetically stable. For non-zero t', we find that orbital antiferromagnetism (or spin nematic) order is stable over a finite portion of the phase diagram at weak coupling. This region of stability is seen to grow with increasing values of t'.