Charge and spin excitation spectra in the one-dimensional Hubbard model with next-nearest-neighbor hopping

TL;DR

This study uses the dynamical density-matrix renormalization group to analyze spin and charge excitation spectra in a 1D Hubbard model with next-nearest-neighbor hopping, revealing the influence of small nearest-neighbor hopping on correlations.

Contribution

It demonstrates how next-nearest-neighbor hopping dominates the excitation spectra and highlights the role of small nearest-neighbor hopping in enhancing ferromagnetic and spin-triplet pairing correlations.

Findings

Excitation spectra resemble those of the 1D Hubbard chain at quarter filling.

Small nearest-neighbor hopping enhances ferromagnetic correlations.

Spin-triplet pairing correlations are induced by the hopping.

Abstract

The dynamical density-matrix renormalization group technique is used to calculate spin and charge excitation spectra in the one-dimensional (1D) Hubbard model at quarter filling with nearest-neighbor $t$ and next-nearest-neighbor $t'$ hopping integrals. We consider a case where $t$ ($>0$) is much smaller than $t'$ ($>0$). We find that the spin and charge excitation spectra come from the two nearly independent $t'$-chains and are basically the same as those of the 1D Hubbard (and t-J) chain at quarter filling. However, we find that the hopping integral $t$ plays a crucial role in the short-range spin and charge correlations; i.e., the ferromagnetic spin correlations between electrons on the neighboring sites is enhanced and simultaneously the spin-triplet pairing correlations is induced, of which the consequences are clearly seen in the calculated spin and charge excitation spectra at low energies.