1998
DOI: 10.1088/0305-4470/31/2/024
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Integrable multiparametric quantum spin chains

Abstract: Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions. We illustrate how this general formalism applies to construct multiparametric versions of the supersymmetric t-J and U models.

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Cited by 23 publications
(28 citation statements)
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“…For instance, it was recently shown [62] that the quantum algebraic structure of the spin 1/2 XXZ chain with twisted periodic boundary conditions is a two-parameter deformed algebra SU q,t (2). Another example is that the work of Reshetikhin [70] on multiparametric quantum algebras was used to construct integrable multiparametric quantum spin chains [39,40]. Hence, possible applications of the Fibonacci oscillator algebra with SU q 1 /q 2 (n)-symmetry in the framework of integrable models with twisted boundary conditions would be another direction of this study which would provide new results for investigations related with correlated electron systems.…”
Section: Discussionmentioning
confidence: 99%
“…For instance, it was recently shown [62] that the quantum algebraic structure of the spin 1/2 XXZ chain with twisted periodic boundary conditions is a two-parameter deformed algebra SU q,t (2). Another example is that the work of Reshetikhin [70] on multiparametric quantum algebras was used to construct integrable multiparametric quantum spin chains [39,40]. Hence, possible applications of the Fibonacci oscillator algebra with SU q 1 /q 2 (n)-symmetry in the framework of integrable models with twisted boundary conditions would be another direction of this study which would provide new results for investigations related with correlated electron systems.…”
Section: Discussionmentioning
confidence: 99%
“…͑For a general construction of multiparametric models, see Ref. 15.͒ For the purposes of the present work, it is necessary to only retain one parameter. The R-matrix is as follows:…”
Section: Generalized Su"1ͦ3… Spin Ladder Modelmentioning
confidence: 99%
“…The free parameter arises in the models as a special choice of the multiparametric versions. 15 In Ref. 16, we note the study of a family of spin ladder Hamiltonians which also have free parameters, although in this case the construction has a different mathematical origin.…”
Section: Introductionmentioning
confidence: 99%
“…They underly elliptic quantum algebras [17][18][19][20][21][22] which play an important role in obtaining solutions to the dynamical Yang-Baxter equations 23,24 and also twisting lies at the core of the construction of multiparametric quantum spin chains. 25 In the context of knot theory, Altschuler and Coste 26 have identified the corresponding ribbon quasi-Hopf algebras as the necessary underlying algebraic structure to study tangle invariants ͑including closed link invariants͒. Here we wish to make two important observations to this field of study.…”
Section: Introductionmentioning
confidence: 99%