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arXiv:cond-mat/9801175 · Journal of Physics A Mathematical and General

Integrable multiparametric quantum spin chains

Angela Foerster, Jon Links, I. Roditi

Published Jan 16, 1998• 19 citations
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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.

DOI
10.1088/0305-4470/31/2/024

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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.
We construct an open quantum spin chain from the “twisted” [Formula: see text]R matrix in the fundamental representation which has the quantum algebra symmetry Uq[ su (2)]. This anisotropic spin-1 chain is different from the Uq[ su (2)]-invariant chain constructed from the “untwisted” [Formula: see text] spin-1 R matrix (namely, the spin-1 XXZ chain of Fateev-Zamolodchikov with boundary terms) but, nevertheless, is also completely integrable. We discuss the general case of an R matrix of the type g(k), where k∈{1, 2, 3}, and g is any simple Lie algebra.
The integrability of the one-dimensional long-range supersymmetric t-J model has previously been established for both open systems and those closed by periodic boundary conditions through explicit construction of its integrals of motion. Recently the system has been extended to include the effect of magnetic flux, which gives rise to a closed chain with twisted boundary conditions. While the t-J model with twisted boundary conditions has been solved for the ground state and full energy spectrum, proof of its integrability has so far been lacking. In this paper we extend the proof of integrability of the long-range supersymmetric t-J model and its SU(m|n) generalization to include the case of twisted boundary conditions.
Exact physical quantities of the D2(2) {D}_2^{(2)} D2(2)​ spin chain model with generic open boundary conditions
A bstract We study the quantum integrable spin chain model associated with the twisted D2(2) {D}_2^{(2)} D2(2)​ D 2 2 algebra (or simply the D2(2) {D}_2^{(2)} D2(2)​ D 2 2 model) under generic open boundary conditions. The Hamiltonian of this model can be factorized into the sum of two staggered XXZ spin chains. Applying the t - W method, we derive the homogeneous Bethe ansatz equations for the zeros of the transfer matrix eigenvalues and the patterns of the corresponding zeros of the staggered XXZ spin chain with generic integrable boundaries. Based on these results, we analytically compute the surface energies and excitation energies of the D2(2) {D}_2^{(2)} D2(2)​ D 2 2 model in different regimes of boundary parameters.