Partial suppression of magnetism in the square lattice SU(3) Hubbard model

Abstract

The SU(N) Hubbard model is a natural extension of the SU(2) model. However, even the N=3 case remains poorly understood. We report a substantially new ground-state phase diagram of the square lattice SU(3) Fermi-Hubbard model. Using a backflow ansatz, we identify strong signatures of a Mott transition and a subsequent magnetic transition, and the suppression of a previously predicted magnetic phase. We study the hole-doped model, identifying a transition from magnetic to paramagnetic behavior in the strong-coupling regime. Our findings offer a qualitatively new ground state picture. More broadly, our work suggests a path to study general SU(N) Hubbard models with arbitrary filling and geometry.

Figures (5)

• Figure 1: Phase diagram. An illustration of the different magnetic phases obtained in this work. The top row shows an illustration of the classical flavor states, the bottom panels sketch the momentum distribution in each phase. Only the paramagnet (PM) is characterized by a sharp Fermi surface.
• Figure 2: Energy comparison. The energy per site for each of the PM, AF32, AF34, and AF33 states, calculated at each value of $U$. Energy is given relative to the energy of the AF34 state. Error-bars are smaller than the markers where not visible. Left: Results obtained with the Slater-Jastrow ansatz. Insets show the different magnetic order patterns of each phase. Right: Results obtained with the backflow ansatz. Inset zooms into the strong-coupling region.
• Figure 3: Structure factor. Structure factor $S(\boldsymbol{k})$ evaluated at the 3 representative momenta, in the lowest energy backflow state at each $U$ (indicated by the background shade). Error-bars are smaller than the markers where not visible.
• Figure 4: Number of doubly occupied sites and quasiparticle weight. Top: The density of doubly occupied sites $D$, evaluated in the lowest energy state at each $U$. Error-bars are smaller than the markers where not visible. Bottom: The quasiparticle weight $Z$ at each $U$. Insets show the Fermi sea at two representative points, with white lines indicating the positions and directions around which we calculate the discontinuity corresponding to the quasiparticle weight.
• Figure 5: Doped energy diagram and structure factor. Top: Energy per site calculated of the AF33 state relative to the PM state, at a range of hole concentrations, and for both $U=8.75\,t$ and $U=10.25\,t$. Calculations were performed using the Slater-Jastrow ansatz. Bottom: Corresponding flavor structure factor, with the same color code as Figure \ref{['fig:spin']}. Error-bars are smaller than the markers where not visible.