Magnetic phase diagram of the Hubbard model in the Lieb lattice

• We study the magnetic phase diagram of the Hubbard model in the Lieb lattice.
• Far from half-filling, we find paramagnetism and ferromagnetism.
• At half-filling the ground state is ferrimagnetic, in agreement with Lieb's theorem.
• The total magnetization approaches Lieb's prediction only as U/t becomes large.
• Away from half-filling, discontinuous transitions to spiral phases are observed.

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 (1991) [1]. At half-filling, the ground state was found to be ferrimagnetic [a (π,π)(π,π) spiral phase], in agreement with a theorem by Lieb (1989) [2]. The total magnetization approaches Lieb's prediction as U/t   becomes large. As we move away from half-filling, this ferrimagnetic phase becomes a (q1,q1)(q1,q1) spiral phase with q1≈πq1≈π and then undergoes a series of first-order phase transitions, (q1,q1)→(q1,q2)→(q1,0)(q1,q1)→(q1,q2)→(q1,0), with q2≈π/2q2≈π/2, before becoming ferromagnetic at large U/t or paramagnetic at low U/t.