A half-filled one-dimensional (1D) extended Hubbard model (U-V_⊥-V_∥) with on-site and nearest-neighbor spin-dependent interactions is studied analytically. The ground state phase diagram is obtained in the weak-coupling regime by performing the bosonization and renormalization group methods. The result shows that the nearest-neighbor spin-dependent attraction influences the low-energy physics of the 1D correlated electron system, and changes the topological structure of the ground state phase diagram of the U-V model.
A one-dimensional model of interacting electrons with on-site U, nearest- neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, \U - 2V\ < \2W\ and a bond-spin-density-wave (BSDW) for W > 0, \U - 2V\ < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the eta(pi) -superconducting phase at \U - 2V\ much less than 2t less than or equal to W is briefly discussed.
Phase diagrams of the one-dimensional extended Hubbard model with a nearest neighbor interaction
V and site-off-diagonal (bond-charge
X and bond-bond
W) interactions at half-filling are obtained numerically, using the level-crossing approach for finite-size clusters. This analysis is straightforward extension of the preceding work [cond-mat/9909277], where only the
X term is considered as a site-off-diagonal term. Similarly to the
X term, the
W term enlarges bond-charge-density-wave (BCDW) and bond-spin-density-wave (BSDW) phases for
W<0 and
W>0 cases, respectively. In the strong-coupling region, however, the
W term causes ferromagnetism for
W>0, and shifts the boundary of the phase separation in the
U/t≪−1 region, which are different from the roles of the
X term. In addition, we discuss a parameter region where the BSDW state is the exact ground state, and show that the exactly solvable point appears just on the phase boundary between the BSDW and the ferromagnetic phases.
A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and correlated-hopping interaction
T∗ is studied at half filling using the continuum-limit field theory approach. The ground-state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin- and charge-density wave phases for large U and V, respectively, we identify bond-located ordered phases corresponding to an enhanced Peierls instability in the system for ${T}^{*}>0, |U\ensuremath{-}2V|<{8T}^{*}/\ensuremath{\pi}$ and to a staggered magnetization located on bonds between sites for ${T}^{*}<0, |U\ensuremath{-}2V|<8|{T}^{*}|/\ensuremath{\pi}.$ The general ground-state phase diagram including insulating, metallic, and superconducting phases is discussed.
We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the weak-coupling renormalization-group approach ( g-ology) to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.
We study the phase diagram of a one-dimensional extended Hubbard model with antiferromagnetic exchange interaction analytically and numerically. The bosonization and transfer-matrix renormalization group methods are used in the corresponding coupling regimes. At half-filling, the system is a Mott insulator with a finite spin excitation gap if the on-site Coulomb repulsion is fairly smaller than the antiferromagnetic exchange
J. This Mott insulator is characterized by the bond-charge-density-wave order or spontaneously dimerization. In the weak-coupling regime where the spin-charge separation holds approximately, the critical point separating the gapless and gapped spin liquid phases is ${U}_{c}\ensuremath{\sim}J∕2$. However, as
J increases, the spin-charge couplings become important and the critical point
Uc is significantly suppressed and eventually tends to zero as $J\ensuremath{\rightarrow}\ensuremath{\infty}$. Away from half-filling, the charge gap completely collapses but the spin gap persists.