Half-filled One-dimensional Extended Hubbard Model Research Articles

Comment on “Accurate ground-state phase diagram of the one-dimensional extended Hubbard model at half filling”

It is shown that Guoping Zhang's results [G. P. Zhang, Phys. Rev. B 68, 153101 (2003)] for the charge-density wave-phase boundary in the half-filled one-dimensional extended Hubbard model are incorrect and that his criticism of my work [E. Jeckelmann, Phys. Rev. Lett. 89, 236401 (2002)] is groundless.

Dimerization in a half-filled one-dimensional extended hubbard model.

We use a density-matrix renormalization group method to study quantitatively the phase diagram of a one-dimensional extended Hubbard model at half filling by investigating the correlation functions and structure factors. We confirmed the existence of a novel narrow region with long-range bond-order-wave order that was highly controversial recently between the charge-density-wave phase and Mott insulator phase. We determined accurately the position of the bicritical point U(b) approximately 7.2t, V(b) approximately 3.746t, which is quite different from previous studies.

Ground state phases of the half-filled one-dimensional extended hubbard model.

Using quantum Monte Carlo simulations, results of a strong-coupling expansion, and Luttinger liquid theory, we determine quantitatively the ground state phase diagram of the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsions U and V. We show that spin frustration stabilizes a bond-ordered (dimerized) state for U approximately V/2 up to U/t approximately 9, where t is the nearest-neighbor hopping. The transition from the dimerized state to the staggered charge-density-wave state for large V/U is continuous for U < or approximately 5.5 and first order for higher U.

Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model

We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach $(g$-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for $U\ensuremath{\approx}2V$ in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line. In the second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential $\ensuremath{\Delta}$ or bond alternation $\ensuremath{\delta}.$ Although the alternating site potential $\ensuremath{\Delta}$ strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. $83,$ 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation $\ensuremath{\delta}$ destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with $\ensuremath{\delta}$ contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of $\ensuremath{\Delta}$ or $\ensuremath{\delta}$ changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.

Ground-state phase diagram of a half-filled one-dimensional extended hubbard model.

The density-matrix renormalization group is used to study the phase diagram of the one-dimensional half-filled Hubbard model with on-site (U) and nearest-neighbor (V) repulsion and hopping t. A critical line V(c)(U) approximately U/2 separates a Mott insulating phase from a charge-density-wave phase. The formation of bound charge excitations for V>2t changes the phase transition from continuous to first-order at a tricritical point U(t) approximately 3.7t, V(t)=2t. A frustrating effective antiferromagnetic spin coupling induces a bond-order-wave phase on the critical line V(c)(U) for U(t)<U less, similar 7t.

Excitons in the strong coupling limit of the one-dimensional extended Hubbard model

Excitons in the strong coupling limit of the half-filled one-dimensional extended Hubbard model with $1/r$ interactions are studied. Unlike the situation for nearest neighbor interactions, where there is at most only one (doubly degenerate) bound state, a $1/r$ interaction results in an infinite number of doubly degenerate bound states. In the continuum limit the exciton states are one-dimensional hydrogenlike states, with binding energies $\ensuremath{\sim}{1/n}^{2}.$ The particle--hole separation grows rapidly with n as ${n}^{2}.$ The binding energies are reduced on a discrete lattice. However, for conjugated systems of interest, the discrete correction to the continuum limit are small. When the infinite onsite repulsion limit is relaxed the degenerate states split, forming a doublet of even and odd parity states.

Exact Bond-Located Spin Ground State in the Hubbard Chain with Off-Diagonal Coulomb Interactions

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.

Effect of Localization on a One-Dimensional Half-Filled Extended Hubbard Model

By use of the method in the previous paper [J. Phys. Soc. Jpn. 53 (1984) 3918], we study the Anderson localization in a one-dimensional half-filled extended Hubbard model with randomness. A transition from localization into delocalization takes place as the attractive interaction for superconductivity increases. It is shown that the effect of localization on singlet superconductivity (SS) is stronger than that on triplet superconductivity (TS) due to the large quantum fluctuation of TS compared with that of SS.