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Magnetic phase diagram of the Hubbard model in the Lieb lattice

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 $(π,π)$ 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 $q_1 \approx π$ and then undergoes a series of first-order phase transitions, $(q_1,q_1) \rightarrow (q_1,q_2) \rightarrow (q_1,0)$, with $q_2 \approx π/2$, before becoming ferromagnetic at large $U/t$ or paramagnetic at low $U/t$.