Generalized Schrieffer-Wolff transformation of multi-flavor Hubbard models

TL;DR

This paper derives the low-energy effective interactions in the SU(N) Hubbard model using a generalized Schrieffer-Wolff transformation, revealing the significance of doublon-holon interactions in spectral features near the Mott transition.

Contribution

It introduces a self-contained derivation of effective interactions in the multi-flavor Hubbard model, emphasizing the role of doublon-holon interactions often overlooked in previous studies.

Findings

Effective doublon-holon interactions cause peaks in the local density of states.

The derivation explains subpeaks at the edges of Hubbard bands near the Mott transition.

The work generalizes SWT to multi-flavor models, broadening its applicability.

Abstract

We give a self-contained derivation of the low-energy effective interactions of the SU($N$) Hubbard model, a multiflavor generalization of the one-band Hubbard model, by using a generalized Schrieffer-Wolff transformation (SWT). The effective interaction of doublons and holons, which has been largely ignored in previous SWT studies (e.g., the $t$-$J$ model), leads to distinct peaks in the local density of states. As shown by Lee et al. [Phys. Rev. Lett. 119, 236402 (2017)], this underlying effective doublon-holon interaction explains the numerical observation of the subpeaks at the inner edges of the Hubbard bands in the metallic phase close to the Mott transition.