Finite-size studies of phases and dimerization in one-dimensional extended Peierls-Hubbard models

Abstract

We study extended Hubbard and Peierls-Hubbard models with up to N =10 sites and half-filled bands with modified boundary conditions. For the extended Hubbard model, the finite-size dependence of the transition from the charge-density-wave regime (CDW) to the spin-density-wave (SDW) regime and of the condensation transition is critically examined, clarifying some previous results. For the Peierls-Hubbard model and N 10 with modified periodic boundary conditions, we always see a decrease of dimerization with U. Extrapolating these results to infinite N, we find that dimerization is enhanced by U for small electron-phonon coupling a &0.75, whereas it decreases with U for 0.75 (a~1. By extending this model by a nearest-neighbor repulsion V, the amplitude of dimerization reaches a maximum at the same value U 2V, where the CDW-to-SDW transition occurs in the extended Hubbard mode;l.

Collective quantum tunneling of strongly correlated electrons in commensurate mesoscopic rings

“…The HOMO-LUMO gap vanishes in the thermodynamic limit, but it is difficult in general to make it much smaller than other energies for sizes (N ∼ 10) for which exact diagonalization can be applied. The HOMO-LUMO gap vanishes identically only in two cases: for sizes N = 4n by imposing periodic boundary conditions (PBC, c N +l,σ ≡ c l,σ ) as well as for N = 4n + 2 and antiperiodic (Möbius) boundary conditions (ABC, c N +l,σ ≡ −c l,σ ) (n is an integer) [2,8,13]. Below, we shall always use these combinations of N -values and boundaries (open shell case).…”

“…An infinite system of noninteracting electrons possesses a divergent density of states at the Fermi level, and this plays a key role for the occurrence of various types of ordering specific for the physics in one dimension: Peierls dimerization, CDW, SDW, etc. In a finite system, such orderings are favored by small values of the energy difference between the lowest unoccupied orbital and the highest occupied orbital (the so called HOMO-LUMO gap [12]) [2,8,13]. The HOMO-LUMO gap vanishes in the thermodynamic limit, but it is difficult in general to make it much smaller than other energies for sizes (N ∼ 10) for which exact diagonalization can be applied.…”

“…The previous studies devoted to this case have paid much attention to the CDW-SDW critical line [5][6][7][8]. Another possible ordering is the charge separation (CS) [8,10]. The interest in this phase was recently revived in the context of strip formation in certain cuprates.…”

“…In the case of a halffilled band two ordered phases are most relevant for quasi one-dimensional compounds: the charge-and spin-densitywaves (CDW, SDW). The previous studies devoted to this case have paid much attention to the CDW-SDW critical line [5][6][7][8]. Another possible ordering is the charge separation (CS) [8,10].…”

Alternating charge densities, peierls distortion, and charge‐conjugation symmetry in correlated one‐dimensional diatomic systems

“…The chosen value of p corresponds to the dimensionless electron-lattice coupling g = p / a equal to 0.5 compared with g = 0.37, the estimation obtained for polyacetylene within the framework of the same approach [ll] and g = 0.39 as found in the exact diagonalization study [15]. The ring boundary conditions are used to exclude the end effects.…”