Magnetic phase diagram of the Hubbard model in the Lieb lattice

TL;DR

This study maps the magnetic phases of the Hubbard model on the Lieb lattice, revealing transitions from paramagnetic to ferromagnetic and ferrimagnetic states depending on electron filling and interaction strength.

Contribution

It provides the first detailed mean-field phase diagram of the Hubbard model on the Lieb lattice, including new insights into phase transitions and magnetic ordering.

Findings

Paramagnetism dominates at low U/t far from half-filling.

Ferrimagnetic phase at half-filling aligns with Lieb's theorem.

Sequence of phase transitions from ferrimagnetic to ferromagnetic or paramagnetic as U/t varies.

Abstract

We study the mean-field phase diagram of the repulsive Hubbard model in the Lieb lattice. Far from half-filling, the most stable phases are paramagnetism for low on-site interaction $U/t$ and ferromagnetism for high $U/t$, as in the case of the mean-field phase diagram of the square lattice Hubbard model obtained by Dzierzawa [\onlinecite{Dzierzawa1992}]. At half-filling, the ground state was found to be ferrimagnetic [a $(\pi,\pi)$ spiral phase], in agreement with a theorem by Lieb [\onlinecite{Lieb1989}]. The total magnetization approaches Lieb's prediction as $U/t$ becomes large. As we move away from half-filling, this ferrimagnetic phase becomes a $(q_1,q_1)$ spiral phase with $q_1 \approx \pi$ and then undergoes a series of first-order phase transitions, $(q_1,q_1) \rightarrow (q_1,q_2) \rightarrow (q_1,0)$, with $q_2 \approx \pi/2$, before becoming ferromagnetic at large $U/t$ or paramagnetic at low $U/t$.