We analyze the charge fluctuations in the two-dimensional quarter-filled extended Hubbard model on an anisotropic triangular lattice. We formulate the patch functional-renormalization-group method for this system and examine the full momentum dependence of the charge/spin susceptibilities. Two distinct peak structures in the charge susceptibility are obtained, where one is due to the Fermi-surface nesting condition and the other is due to the intersite Coulomb repulsions. It is shown that the mode-coupling effects within the particle-hole channel are crucial to improve the results of the random-phase-approximation, while the mode-coupling effects involving the particle-particle channel do not have strong effects. The validity of the random-phase-approximation is also discussed.
Using a high-frequency expansion in periodically driven extended Hubbard models, where the strengths and ranges of density-density interactions are arbitrary, we obtain the effective interactions and bandwidth, which depend sensitively on the polarization of the driving field. Then, we numerically calculate modulations of correlation functions in a quarter-filled extended Hubbard model with nearest-neighbor interactions on a triangular lattice with trimers after monocycle pulse excitation. We discuss how the resultant modulations are compatible with the effective interactions and bandwidth derived above on the basis of their dependence on the polarization of photoexcitation, which is easily accessible by experiments. Some correlation functions after monocycle pulse excitation are consistent with the effective interactions, which are weaker or stronger than the original ones. However, the photoinduced enhancement of anisotropic charge correlations previously discussed for the three-quarter-filled organic conductor
α-(bis[ethylenedithio]-tetrathiafulvalene)
2I
3 [
α-(BEDT-TTF)
2I
3] in the metallic phase is not fully explained by the effective interactions or bandwidth, which are derived independently of the filling.
The extended Hubbard model in an anisotropic triangular lattice is analyzed at quarter filling by the functional renormalization group (fRG) approach. We obtain the finite temperature phase diagram in the plane of nearest inter-site Coulomb interaction Vp and next-nearest Coulomb interaction Vc. When Vp ? Vc, charge order does not occur down to the low temperature of 0.1tp, where the tp is the electron transfer between the nearest neighbor sites. We interpret the result using the random-phase approximation(RPA).