Tomonaga-Luttinger parameters and spin excitations in the dimerized extended Hubbard model

TL;DR

This study investigates the effects of dimerization and interactions on the spin and charge excitations in a one-dimensional extended Hubbard model, revealing how gaps and correlations evolve with doping and interaction strength.

Contribution

It provides a detailed analysis of the Tomonaga-Luttinger parameters and excitation gaps in the dimerized extended Hubbard model using DMRG, highlighting new insights into charge-density-wave formation and spin-charge separation.

Findings

Gaps in spin and charge excitations vanish with hole doping.

Charge-density-wave ground state emerges beyond a critical interaction.

Dimerization and Coulomb interaction significantly reduce the Tomonaga-Luttinger parameter.

Abstract

We study the one-dimensional extended Hubbard model with alternating size of the hopping integrals using the density-matrix renormalization group method. We calculate the spin gap, the Tomonaga-Luttinger parameter, and the charge-density-wave order parameter for various dimerizations, interaction strengths, and band fillings. At half band-filling the spin and charge excitations are gapped but these gaps disappear for infinitesimal hole doping. At quarter filling, the Umklapp scattering in the half-filled lower Peierls band generates a gap for the charge excitations but the gapless spin excitations can be described in terms of an effective antiferromagnetic Heisenberg model. Beyond a critical strength for the nearest-neighbor interaction, the dimerized extended Hubbard model at quarter filling develops a charge-density-wave ground state. The dimerization and the nearest-neighbor Coulomb interaction strongly reduce the Tomonaga-Luttinger parameter from its value for the bare Hubbard model. We discuss the relevance of our findings for the Bechgaard salts.