We show the existence of an exact ground state in certain parameter regimes of one-dimensional half-filled extended Hubbard model with site-off-diagonal interactions. In this ground state, the bond-located spin correlation exhibits a long-range order. In the case when the spin space is SU(2) symmetric, this ground state degenerates with higher spin states including a fully ferromagnetic state. We also discuss the relation between the exact bond-ordered ground state and the critical bond-spin-density-wave phase.
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.
Using the field theoretical bosonization and renormalization group techniques, we analytically study quantum phase diagram of a one-dimensional half-filled extended Hubbard model with on-site (U) and spin-dependent nearest-neighbor interactions (V⊥, V‖) in the weak coupling regime. In the case of easy-plane anisotropy (V⊥ > V‖) and at V‖ < U/2, the existence of bond-ordered spin-density-wave phase, corresponding to spin gapless transverse magnetization located on bonds (BSDW±) is shown.
We discuss global structures of ground-state phase diagrams in a one-dimensional half-filled electron system with on-site and spin-dependent nearest-neighbor-site Coulomb interactions. We compare our numerical calculation data for phase boundary lines with their analytical expressions in three limiting regions of interaction parameters and find good agreement between them. In the intermediate-coupling region, however, we observe nontrivial structures of phase diagrams: For systems with weak easy-plain anisotropy, both the bond-located spin- and charge-density-wave phases are realized. The latter contacts with the ferromagnetic phase stabilized in the strong-coupling region. On the other hand, when anisotropy becomes large, the intermediate phase disappears and consequently a direct transition between the former and ferromagnetic phase is observed.
We study the effects of a bond-charge interaction (or correlated hopping) on the properties of the extended [i.e., with both on-site (U) and nearest-neighbor (V) repulsions] Hubbard model in one dimension at half-filling. Energy gaps and correlation functions are calculated by Lanczos diagonalization on finite systems. We find that, irrespective of the sign of the bond-charge interaction, X, the charge-density-wave (CDW) state is more robust than the spin-density-wave (SDW) state. A small bond-charge interaction term is enough to make the differences between the CDW and SDW correlation functions much less dramatic than when X=0. For X=t and fixed V2t (t is the uncorrelated hopping integral), there is an intermediate phase between a charge ordered phase and a phase corresponding to singly occupied sites, the nature of which we clarify: it is characterized by a succession of critical points, each of which corresponds to a different density of doubly occupied sites. We also find an unusual slowly decaying staggered spin-density correlation function, which is suggestive of some degree of ordering. No enhancement of pairing correlations was found for any X in the range examined. \textcopyright{} 1996 The American Physical Society.
We consider a generalized Hubbard model with on-site interaction U, nearest-neighbor repulsion V, and nearest-neighbor hopping for spin \ensuremath{\sigma}, which depends on the sum of particles ${\mathrm{m}}_{\mathrm{\ensuremath{\sigma}}\ensuremath{-}|\mathrm{A}\mathrm{m}}$ with opposite spin in the two sites involved. The hopping matrix elements are denoted by
tAA,
tAB,
tBB for ${\mathrm{m}}_{\mathrm{\ensuremath{\sigma}}\ensuremath{-}|\mathrm{A}\mathrm{m}}$=0,1,2, respectively. For 0
tABtAA=
tBB, we have determined the regions of parameters for which the ground-state (GS) of the one-dimensional system is a charge-density wave (CDW), a spin-density wave (SDW), or a metal (M), using Hartree-Fock, exact diagonalization of finite chains and quantum Monte Carlo. The results agree qualitatively with the exactly solvable limit of
tAB=0. For 0
tABtAA=
tBB, the GS is a M for sufficiently low values of U and V. In contrast, when
tAA+
tBB-
2tAB=0, our results suggest that the GS is either a CDW or a SDW, with the boundary between them lying near the line U=2V.