Coexistence of distinct charge fluctuations in $\theta \text{−}{\left(\text{BEDT-TTF}\right)}_2\text{X}$

Using the Lanczos exact-diagonalization and density-matrix renormalization-group methods, we study the extended Hubbard model at quarter filling defined on the anisotropic triangular lattice. We focus on charge ordering (CO) phenomena induced by onsite and intersite Coulomb interactions. We determine the ground-state phase diagram including three CO phases, i.e., diagonal, vertical, and threefold CO phases, based on the calculated results of the hole density and double occupancy. We also calculate the dynamical density-density correlation functions and find possible coexistence of the diagonal and threefold charge fluctuations in a certain parameter region where the onsite and intersite interactions compete. Furthermore, the characteristic features of the optical conductivity for each CO phase are discussed.

Figure 1

(Color online) Schematic representation of the anisotropic triangular-lattice Hubbard model. Each circle denotes an ET molecule and $\theta$ is an angle between the ET molecular planes of the adjacent stacks. We take $t_p=1$ as the unit of energy.

Figure 2

(Color online) Hole density $⟨n_i⟩$ and double occupancy $⟨d_i⟩$ at the hole-rich sites for (a) $V_p=1$, (b) $V_c=1$, and (c) $V_p=V_c$. The inset shows the schematic representation of (a) the vertical stripe, (b) diagonal stripe, and (c) threefold CO patterns. The solid circle denotes a site where the hole predominantly resides. The other configurations are also shown: (d) horizontal and (e) an example of randomly aligned CO patterns.

Figure 3

(Color online) Ground-state phase diagram of the extended Hubbard model defined on the anisotropic triangular lattice. We assume the values $t_c=0$ and $U=10$. The result is obtained from the DMRG calculations for the charge distributions with a broken translational symmetry. The diameter of the circles is taken to be proportional to $⟨n_{i∊\text{rich}}⟩-0.5$.

Figure 4

(Color online) Transition between diagonal and threefold CO states. The solid circle denotes a site where hole predominantly resides. The arrows denote the flow of charges toward the other CO state.

Figure 5

(Color online) Charge excitation spectra calculated for the 18-site cluster with the Lanczos exact-diagonalization method. Only the results of $\left(\pi ,0\right)$ are obtained for the 16-site cluster. Spectra at $\left(V_p,V_c\right)=\left(1,5\right)$ and $\left(5,1\right)$ (left panel) and (0,0), (3,3), and (5,5) (right panel) are shown.

Figure 6

(Color online) Single-particle excitation spectra calculated for the 18-site cluster with the Lanczos exact-diagonalization method. The dashed lines denote the Fermi levels and the thin lines mark the dispersion of bands.

Figure 7

(Color online) Optical conductivity spectra calculated with the DDMRG method. $\alpha \left(=a,c\right)$ is the direction of the electric field defined in Fig. 1.