Geometrical frustration of an extended Hubbard diamond chain in the quasiatomic limit

We study the geometrical frustration of an extended Hubbard model on a diamond chain, where vertical lines correspond to the hopping and repulsive Coulomb interaction terms between sites while the remaining lines represent only the Coulomb repulsion term. The phase diagrams at zero temperature show quite curious phases: five types of frustrated states and four types of nonfrustrated states, ordered antiferromagnetically. Although a decoration transformation was derived for spin-coupling systems, this approach can be applied to electron-coupling systems. Thus the extended Hubbard model can be mapped onto another effective extended Hubbard model in the atomic limit with additional three- and four-body couplings. This effective model is solved exactly using the transfer-matrix method. In addition, using the exact solution of this model, we discuss several thermodynamic properties away from the half-filled band, such as chemical potential behavior, electronic density, and entropy, for which we study geometrical frustration. Consequently, we investigate the specific heat as well.

Figure 1

Schematic representation of the extended Hubbard model on a diamond chain.

Figure 2

Phase diagrams at zero temperature: (a) the phase diagram of $V/U$ vs $\mu /U$ for a fixed value of $t/U=1$; (b) the phase diagram of $t/U$ vs $\mu /U$ for a fixed value of $V/U=0.25$.

Figure 3

Electronic density per site for $T/U=0.01$ and $V/U=0.1$ as a function of $t/U$ and $\mu /U$. The black region corresponds to empty particles while the white region corresponds to fully filled electrons or empty holes. Different levels of gray represent the intermediate electronic density.

Figure 4

Electronic density as a function of chemical potential for a fixed value of $V/U=0.1$. (a) $t/U=0.5$ and (b) $t/U=2.0$

Figure 5

Internal energy $\mathcal{E}\left(\rho \right)$ as a function of electronic density $\rho$ for a given value of $V/U=0.1$. (a) $t/U=0.2$ and (b) $t/U=0.5$

Figure 6

The compressibility $\kappa \left(\rho \right)$ as a function of electronic density $\rho$ for a fixed value of $V/U=0.1$. (a) $t/U=0.2$ and (b) $t/U=0.5$.

Figure 7

Entropy as a function of $t/U$ and $\mu /U$ for a fixed value of $U/V=0.1$. The black region corresponds to nonfrustrated entropy while the white region corresponds to the higher residual entropy effect. Gray areas correspond to the intermediate residual entropy effect.

Figure 8

Entropy $\mathcal{S}$ against $\mu$ at low temperature assuming a fixed value of $V/U=0.25$. (a) $t/U=0.2$ and (b) $t/U=0.5$.

Figure 9

Entropy against electronic density assuming fixed Coulomb coupling $V/U=0.1$. (a) $t/U=0.2$ and (b) $t/U=0.5$.

Figure 10

The specific heat vs the chemical potential for low temperature for a fixed value of $V/U=0.25$. (a) $t/U=0.2$ and (b) $t/U=0.5$.

Figure 11

The specific heat vs temperature for a given value of $V/U=0.25$ and different values of chemical potential. (a) $t/U=0.2$ and (b) $t/U=0.5$.