Theory of the lightly doped Mott insulator

A theory for the Hubbard model appropriate in the limit of large $U/t$, small doping away from half-filling and short-ranged antiferromagnetic spin correlations is presented. Despite the absence of any broken symmetry, the Fermi surface takes the form of elliptical hole pockets centered near $\left(\frac{\pi }{2},\frac{\pi }{2}\right)$ with a volume proportional to the hole concentration. Short-range antiferromagnetic correlations render the nearest-neighbor hopping almost ineffective so that only second- or third-nearest-neighbor hopping contributes appreciably to the dispersion relation.

Figure 1

Comparison of the static spin-correlation function ${\chi }_{\mathbf{R}}$ obtained from Eq. (3) with the side condition (4) (lines) to the results of exact diagonalization of 32-site clusters with different hole concentrations $\delta$ (squares, taken from Ref. 29). The values of ${\chi }_{10}$ is $-0.3\left(-0.25\right)$ in the left (right) panel, the values of $\zeta$ are 0.5, 1.0, 2.0, and 4.0 in both figures.

Figure 2

Lower panel: dispersion of the lower band at $\delta =0.1$ for different values of ${\chi }_{10}$. Upper panel: dispersion of the spectral weight of the quasiparticle band. Parameters for the spin-correlation function are $\zeta =4$, $C_0=0.203$ for ${\chi }_{10}=-0.3$ and $\zeta =1$, $C_0=0.0576$ for ${\chi }_{10}=-0.2$.

Figure 3

Fermi surface at $\delta =0.1$ for different values of ${\chi }_{10}$. All parameter values are as in Fig. 2.

Figure 4

Fermi surface at $\delta =0.1$ (top) and band structure for different values of $t_{11}$. The ratio $t_{11}/t_{20}=-2$ is kept fixed, the parameters of the spin-correlation function are ${\chi }_{10}=-0.3$, $\zeta =4$, and $C_0=0.203$.

Figure 5

Shift of the center of the hole pocket ${\kappa }_0$ as a function of the nearest-neighbor spin correlation, ${\chi }_{10}$, for different $t_{11}$. The ratio $t_{11}/t_{20}=-2$ is kept fixed.

Figure 6

Probability $p_v$ for violation of the hard-core constraint as a function of the hole concentration $\delta$. The finite value of $p_v$ at $\delta =0$ is due to the charge fluctuations at half filling.

Figure 7

Comparison of the two sides of Eq. (C1) using data from exact diagonalization of a $4\times 4$ cluster of the t-J model for different $t_{11}$. The ratio $t_{11}/t_{20}=-2$ was kept fixed. Also shown is the quasiparticle weight at $\left(\frac{\pi }{2},\frac{\pi }{2}\right)$.