Competing Orders in the 2D Half-Filled $\mathrm{SU}(2N)$ Hubbard Model through the Pinning-Field Quantum Monte Carlo Simulations

We nonperturbatively investigate the ground state magnetic properties of the 2D half-filled SU($2N$) Hubbard model in the square lattice by using the projector determinant quantum Monte Carlo simulations combined with the method of local pinning fields. Long-range Néel orders are found for both the SU(4) and SU(6) cases at small and intermediate values of $U$. In both cases, the long-range Néel moments exhibit nonmonotonic behavior with respect to $U$, which first grow and then drop as $U$ increases. This result is fundamentally different from the SU(2) case in which the Néel moments increase monotonically and saturate. In the SU(6) case, a transition to the columnar dimer phase is found in the strong interaction regime.

Figure 1

Finite size scaling of the residual Néel moment $m_Q(L)$ vs $1/L$ under pinning fields described by Eq. (3) with $h_{i_0{j}_0}=1$ and 2. The largest value of $L$ is 16. The quadratic polynomial fitting is used. Error bars are smaller than symbols.

Figure 2

Finite size scalings of $m_Q(L)$ vs $1/L$ for the half-filled SU(4) Hubbard model with different values of $U$. The largest size is $L=16$. The quadratic polynomial fitting is used. Error bars of QMC data are smaller than symbols.

Figure 3

Finite size scalings of $m_Q(L)$ vs $1/L$ for the SU(6) Hubbard model at different values of $U$. The largest size is $L=16$. The quadratic polynomial fitting is used. Error bars of QMC data are smaller than symbols.

Figure 4

The ground state Néel ordering of the 2D half-filled $\mathrm{SU}(2N)$ Hubbard model in the square lattice. The relations of long-range Néel moments $m_Q$ vs $U$ are plotted for $2N=2$, 4, and 6. For comparison, the SU(2) Heisenberg limit result is plotted as the dotted line. The error bars are obtained from the least square fittings with $95\%$ confidence bounds.

Figure 5

Finite-size scalings of the dimer order parameters in the half-filled SU(6) Hubbard model. (a) ${\dim }_{(\pi ,0)}(L)$ and (b) ${\dim }_{(\pi ,\pi )}(L)$ at wave vectors $Q^{\prime }=(\pi ,0)$ and $Q=(\pi ,\pi )$, respectively. The largest size is $L=16$. Error bars of QMC data are smaller than symbols.