Generalised integrable Hubbard models

TL;DR

This paper develops generalized integrable Hubbard models based on superalgebras, providing new R-matrices satisfying the Yang-Baxter equation, and analyzing their Hamiltonians, symmetries, and scattering properties.

Contribution

It introduces a unified construction of Hubbard-like models using superalgebras, extending previous models and explicitly deriving their integrability and scattering features.

Findings

R-matrices satisfy Yang-Baxter equation

Explicit Hamiltonians and symmetries derived

Two-particle scattering described

Abstract

We construct the XX and Hubbard-like models based on unitary superalgebras gl(N|M) generalizing Shastry's and Maassarani's approach. We introduce the R-matrix of the gl(N|M) XX-type model; the one of the Hubbard-like model is defined by "coupling" two independent XX models. In both cases, we show that the R-matrices satisfy the Yang-Baxter equation. We derive the corresponding local Hamiltonian in the transfer matrix formalism and we determine its symmetries. A perturbative calculation "\`a la Klein and Seitz" is performed. Some explicit examples are worked out. We give a description of the two-particle scattering.