Super-Hubbard models and applications

TL;DR

This paper develops superalgebra-based XX and Hubbard models, deriving their R-matrices, Hamiltonians, and symmetries, with explicit examples and perturbative analysis for specific cases.

Contribution

It introduces a unified algebraic framework for super-Hubbard models using gl(N|M) superalgebras, extending previous algebraic approaches.

Findings

R-matrices satisfy Yang-Baxter equation

Hamiltonians derived in transfer matrix formalism

Explicit examples and two-loop perturbative analysis

Abstract

We construct XX- and Hubbard- like models based on unitary superalgebras gl(N|M) generalising Shastry's and Maassarani's approach of the algebraic case. We introduce the R-matrix of the gl(N|M) XX model and that of the Hubbard model 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 the symmetry of the Hamiltonian. Explicit examples are worked out. In the cases of the gl(1|2) and gl(2|2) Hubbard models, a perturbative calculation at two loops a la Klein and Seitz is performed.