The Role of the Exchange Interaction in the One-Dimensional $n$-Component Hubbard Model

TL;DR

This paper explores how the exchange interaction influences the electronic phases in a one-dimensional $n$-component Hubbard model, revealing conditions for metallic, insulating, and bond-ordered states through advanced analytical and numerical methods.

Contribution

It demonstrates that the exchange interaction is fundamental in driving bond ordering in the Hubbard model across various interaction strengths.

Findings

Metallic or insulating behavior depends on the relation between $n$ and $q$.

Bond-ordered ground states emerge at specific fillings.

Exchange interaction is crucial for bond ordering at all Coulomb interaction levels.

Abstract

The commensurate $p/q$-filled $n$-component Hubbard chain was investigated by bosonization and high-precision density-matrix renormalization-group analysis. It was found that depending on the relation between the number of components $n$, and the filling parameter $q$, the system shows metallic or insulating behavior, and for special fillings bond-ordered (dimerized, trimerized, tetramerized etc.) ground state develops in the insulating phase. A mean-field analysis shows that this bond ordering is a direct consequence of the spin-exchange interaction, which plays a crucial role in the one-parameter Hubbard model -- not only for infinite Coulomb repulsion, but for intermediate values as well.