Classical and Quantum sl(1|2) Superalgebras, Casimir Operators and Quantum Chain Hamiltonians

Abstract

We examine the two parameter deformed superalgebra $U_{qs}(sl(1|2))$ and use the results in the construction of quantum chain Hamiltonians. This study is done both in the framework of the Serre presentation and in the $R$-matrix scheme of Faddeev, Reshetikhin and Takhtajan (FRT). We show that there exists an infinite number of Casimir operators, indexed by integers $p>1$ in the undeformed case and by $p\in Z$ in the deformed case, which obey quadratic relations. The construction of the dual superalgebra of functions on $S{L}_{qs}(1|2)$ is also given and higher tensor product representations are discussed. Finally, we construct quantum chain Hamiltonians based on the Casimir operators. In the deformed case we find two Hamiltonians which describe deformed $t-J$ models.

27 pages, LaTeX, one reference moved and one formula added

References in corpus (6)

• Integrable open-boundary conditions for the supersymmetric t-J model. The quantum group invariant case
• Finite-dimensional representations of the quantum superalgebra $U_q[gl(n/m)]$ and related q-identities
• Reaction-Diffusion Processes Described by Three-State Quantum Chains and Integrability
• Anyonic FRT construction
• R-matrix Approach to Quantum Superalgebras su_{q}(m|n)
• Generalized $t$-$j$ Model

Cited by in corpus (16)

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• On Combined Standard-Nonstandard or Hybrid (q,h)-Deformations
• Staggered Anisotropy Parameter Modification of the Anisotropic $t-J$ Model
• Centre and Representations of U_q(sl(2|1)) at Roots of Unity
• On boundary super algebras
• Gaudin models with ${\CU}_q(\mathfrak{osp}(1 | 2))$ symmetry
• Integrable Kondo impurities in one-dimensional extended Hubbard models
• The R-matrix of the symplecto-orthogonal quantum superalgebra U_q(spo(2n|2m)) in the vector representation
• Bethe ansatz solution of the anisotropic correlated electron model associated with the Temperley-Lieb algebra
• Yangian and quantum universal solutions of Gervais--Neveu--Felder equations