Resonating-Valence-Bond States and Ferromagnetic Correlations in the Doped Triangular Mott Insulator

The two-dimensional $t$-$J$ model on a triangular lattice is studied using high-temperature expansions. By studying the entropy and spin susceptibility, we find that the sign of the hopping integral $t$ is very crucial. In the case of $t>0$, the peak of the spin susceptibility moves to the high-temperature region with hole doping, which indicates the appearance of the resonating-valence-bond state. In contrast, for $t<0$, the peak of the spin susceptibility disappears with hole doping and the entropy at low temperatures behaves as $S=\gamma T$ with large coefficient $\gamma$, representing a large effective mass. This behavior is understood from the competition between Nagaoka’s ferromagnetism and singlet formation.

Figure 1

(a) The entropy as a function of internal energy and (b) as a function of temperature for the Heisenberg model on the triangular lattice. Various Padé approximations ($[7,4]$, etc.) of $S(e{)}^{3/2}$ are plotted. They converge very well down to $T=0$ and the ground state energy is estimated as $e_0=-0.548\pm 0.003J$. Comparisons with the spin-wave theory are also shown.

Figure 2

(a) The entropy at $J/t=0.4(t>0)$ and $\delta =0–0.8$. For the cases $\delta =0.2,0.4$, and $0.6$, the usual Padé approximation for $S$ is used. (See the text in detail.) (b) The entropy at $J/t=-0.4(t<0)$ and $\delta =0–0.4$.

Figure 3

The spin susceptibility $\chi$ as a function of temperature for $J/t=0.4(t>0)$ and $\delta =0,0.1,0.2,0.3,0.4$. The error bars indicate the scattering of various Padé approximations. The peak of $\chi$ shifts to higher temperatures with hole doping. $\chi$ for $J/t=-0.4(t<0)$, $\delta =0.2$ is also shown.

Figure 4

The spin-spin correlation function $S(q)$ at $k_{B}T=|t|$, $J=0$, $\delta =0.01$. $S(q)$ has a peak at $q=(0,0)$. This ferromagnetic behavior also appears with increasing the doping rate $\delta$.

Figure 5

The eigenvalues and eigenstates of the three-sites $t$-$J$ model with one hole. A couple of two-up spins means a triplet state and that of opposite spins means a singlet state.