Phases of the Infinite $U$ Hubbard Model on Square Lattices

We apply the density matrix renormalization group to study the phase diagram of the infinite $U$ Hubbard model on 2- to 6-leg ladders. Where the results are largely insensitive to the ladder width, we consider the results representative of the 2D square lattice. We find a fully polarized ferromagnetic Fermi liquid phase when $n$, the density of electrons per site, is in the range $1>n\gtrsim 0.800$. For $n=3/4$ we find an unexpected insulating checkerboard phase with coexisting bond-density order with 4 sites per unit cell and block-spin antiferromagnetic order with 8 sites per unit cell. For $3/4>n$, all ladders with width $>2$ have unpolarized ground states.

Figure 1

The phase diagrams of the infinite $U$ Hubbard model on the 2-, 4-, and 6-leg ladders, and the inferred phase diagram in 2D.

Figure 2

Ground-state correlations at $n=3/4$ for a central portion of (a) the $2\times 20$ ladder, (b) the $4\times 20$ ladder, (c) the $6\times 8$ ladder. The thickness of the lines is proportional to the third power of the magnitude of $B_{ij}$, and the length of the arrows to the magnitude of $S_j$, where the axis of spin quantization is set by a Zeeman field of strength $h=1$ applied to the lower left-hand site of each ladder. The numbers index the position along the ladder. For the $2\times 20$ ladder, the values of $B_{ij}$ in the figure range from $B_{ij}=0.30$ (lightest line) to $B_{ij}=0.45$ (darkest line), while the magnitude of $S_j$ ranges from $-0.19$ to 0.21. For the $4\times 20$ ladder $B_{ij}$ ranges from 0.30 to 0.41, while $S_j$ ranges from $-0.12$ to 0.12. For the $6\times 8$ ladder $B_{ij}$ ranges from $B_{ij}=0.31$ to 0.41, while $S_j$ ranges from $-0.18$ to 0.16. (We have obtained similar results for a $6\times 16$ ladder, but even keeping 18 000 states, the convergence is not as complete as for the smaller ladders.)

Figure 3

(a) Magnetization, normalized to its maximum possible value, of the 2-leg ladder as a function of $n$. The four highly overlapping curves correspond, respectively, to $N=50$, 40, 30, and 20. (b) Expectation value of the site density, $n_j$, in a $2\times 50$ ladder with average density $n=0.77$ and a chemical potential of magnitude $\mu =0.3t$ applied to the leftmost $2\times 20$ sites.