One-dimensionalt−Jmodel coupled to adiabatic phonons: A numerical investigation

Abstract

The ground state of the one-dimensional t-J model coupled with phonons in the adiabatic limit is numerically investigated by use of the Lanczos technique at quarter filling. Due to the interplay between the electron-electron Coulomb repulsion and electron-phonon interaction, this model shows a sequence of lattice distortions leading to the formation of charge-density-waves and bondorder-waves. Moderate electron-electron and electron-lattice coupling may lead to coexistence of dimerization and tetramerization in the distortion pattern. Dimerization leads to the formation of an "antiferromagnetic" Mott insulator, while tetramerization gives rise to a spin-Peierls phase. By increasing the super-exchange coupling, antiferromagnetism is inhibited due to the change of the distortion periodicity.

Competitive density waves in quasi-one-dimensional electron systems

“…In all cases the results do not depend on the starting bond configuration nor on the convergence requirement of the adopted iterative method. 9 At large K H , the numerical data show a narrow region where the ground state is a 4k F BOW, as we found in the J → 0 limit. However, we suspect that in the thermodynamic limit this phase disappears at finite J: our evidence for this comes from few Lanczos diagonalizations carried out in a N = 20 site chain 18 showing that the stability region of the 4k F BOW phase is considerably reduced, while the other phase boundaries hardly move.…”

“…However, by reducing the antiferromagnetic coupling or by including a nearest neighbor Coulomb term V, a small BCDW region characterized by the S-W-S-WЈ sequence does appear, as already noticed in a previous investigation. 9 This suggests that in the small J limit, where the t-J model reduces to the strong coupling regime of the Hubbard model, the S-W-S-WЈ bond pattern shows up. 6,19 The sequence of modulations displayed in the phase diagram of Fig.…”

“…In order to find the bond length configuration which minimizes the total energy E({δ i } , {v i }), at fixed spring constants (K B , K H ), we iterate the set of equations (2) until convergence is reached. Following a previous investigation 9 we chose open shell boundary conditions in order to mimic the gapless behavior of the (pure) t − J model in the thermodynamic limit when studying a small size chain (N ≤ 16).…”

“…7 However, the role of phonon coupling in 1D models which may display attractive interactions, like the t-J model, received comparatively less attention. 8,9 The simultaneous presence of both bond and on-site ͑Holstein͒ phonons is likely to be an essential ingredient for a faithful representation of quasi-1D organic materials. In this paper we explore systematically the effect of adding electron-phonon interactions to the t-J model by including intersite ͑bond͒ and onsite ͑Holstein͒ phonon couplings in the adiabatic approximation.…”

“…Recent works extended the study to include quantum effects for the phonons 7 . However, the role of phonon coupling in 1D models which may display attractive interactions, like the t − J model, received comparatively less attention 8,9 . The simultaneous presence of both bond and on-site (Holstein) phonons is likely to be an essential ingredient for a faithful representation of quasi 1D organic materials.…”