Effect of hole doping on the 120 degree order in the triangular lattice Hubbard model: A Hartree-Fock revisit

TL;DR

This study revisits the Hubbard model on a triangular lattice, revealing how hole doping affects magnetic orders, with the 120-degree order persisting up to 0.3 doping and a transition to collinear order and paramagnetism at higher doping levels.

Contribution

It provides a detailed Hartree-Fock phase diagram showing magnetic order evolution with doping, highlighting phase coexistence and transitions in the doped triangular lattice Hubbard model.

Findings

120-degree order persists up to 0.3 doping

A collinear order emerges at 1/3 doping

Phase separation occurs between 120-degree and collinear phases

Abstract

We revisit the unrestricted Hartree Fock study on the evolution of the ground state of the Hubbard model on the triangular lattice with hole doping. At half-filling, it is known that the ground state of the Hubbard model on triangular lattice develops a 120 degree coplanar order at half-filling in the strong interaction limit, i.e., in the spin 1/2 anti-ferromagnetic Heisenberg model on the triangular lattice. The ground state property in the doped case is still in controversy even though extensive studies were performed in the past. Within Hartree Fock theory, we find that the 120 degree order persists from zero doping to about 0.3 hole doping. At 1/3 hole doping, a three-sublattice collinear order emerges in which the doped hole is concentrated on one of the three sublattices with antiferromagnetic Neel order on the remaining two sublattices, which forms a honeycomb lattice. Between the 120 degree order and 1/3 doping region, a phase separation occurs in which the 120 degree order coexists with the collinear anti-ferromagnetic order in different region of the system. The collinear phase extends from 1/3 doping to about 0.41 doping, beyond which the ground state is paramagnetic with uniform electron density. The phase diagram from Hartree Fock could provide guidance for the future study of the doped Hubbard model on triangular lattice with more sophisticated many-body approaches.