Magnetism and infrared divergence in a Hubbard-phonon interacting system

TL;DR

This paper demonstrates that a Hubbard-phonon system exhibits either ferromagnetic or unique spin-singlet ground states under infrared singular conditions, using a unitary transformation and operator algebraic methods.

Contribution

It introduces a concrete infrared singular representation for the system, extending techniques from the van Hove model to Hubbard-phonon interactions.

Findings

Finite Hubbard-phonon systems can have ferromagnetic or spin-singlet ground states.

A new infrared singular representation is constructed using operator algebraic methods.

The approach parallels the van Hove model analysis with Wightman functionals.

Abstract

We show that a finite Hubbard-phonon interacting system has ferromagnetic or unique spin-singlet ground state under the infrared singular condition. The key tool is a unitary transformation introduced by Arai and Hirokawa. We construct a concrete infrared singular representation using the operator algebraic method. The method is essentially same as one for the van Hove model using the Wightman functional method.