Quarter-filled extended Hubbard model with alternating transfer integral: Two-dimensional Ising transition in the ground state

We study the one-dimensional quarter-filled extended Hubbard model with an alternating transfer integral. In the strong-dimerization limit the charge part is described by the quantum Ising model which shows the two-dimensional Ising criticality at the self-dual point, and it is naturally connected to the double-frequency sine–Gordon theory in the weak dimerization. Treating low-lying excitations in finite-size systems, we numerically determine a phase boundary between two types of $4k_{\mathrm{F}}$ density-wave states and clarify the ground-state phase diagram. Further, we refer to its relevances to the charge-ordered phase observed in the charge-transfer organic salts.

Figure 1

The ground-state phase diagram of the quarter-filled EHM with an alternating transfer integral. The correspondence between marks and system sizes is given in the figure. The double circles show the limiting values, i.e., $(V*\left(U\right),0)$ at which criticality changes from the Gaussian to the 2D-Ising type, and (8, 1) the self-dual point.

Figure 2

The $\delta$ dependence of $z_{\rho }\left(L\right)$ at $U=16$ and $V=4$. The vertical dotted line indicates the transition point (i.e., the PRG result) ${\delta }_{\rho }(16,4)\simeq 0.12$. Inset plots $L$ dependences of ${\delta }_{\rho }^{\prime }(U,V,L)$ (crosses) and the PRG data ${\delta }_{\rho }(U,V,L)$ (circles) with the fitting line.