Super-Hubbard models and applications

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.

26 pages

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Cited by in corpus (10)

• Yang-Baxter integrable Lindblad equations
• The Bound State S-matrix of the Deformed Hubbard Chain
• Bethe equations for generalized Hubbard models
• Universal Hubbard models with arbitrary symmetry
• Generalised integrable Hubbard models
• Including a phase in the Bethe equations of the Hubbard model
• Flag Integrable Models and Generalized Graded Algebras
• Lepton masses and mixings in orbifold models with three Higgs families
• Multiplicity in Supersymmetric Spin Chains
• Quantum integrable systems. Quantitative methods in biology