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Acta Physica Sinica

LAX PAIR FORMULATION FOR ONE-DIMENSIONAL-LATTICE SPIN OPEN CHAINS

Huan-Qiang Zhou, 重庆大学应用物理系

Published Jan 1, 1997• 0 citations
Publisher

Abstract

The Lax pair formulation is presented for quantum completely integrable lattice spin open chains.Specifically,the Lax pair for the one-dimensional Heisenberg XXZ open chain with the general boundary terms is explicitly constructed.The construction provides an alternative and direct demonstration for the quantum integrability of the system.

DOI
10.7498/aps.46.140

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The Lax pair formulation is presented for quantum completely integrable lattice spin open chains.Specifically,the Lax pair for the one-dimensional Heisenberg XXZ open chain with the general boundary terms is explicitly constructed.The construction provides an alternative and direct demonstration for the quantum integrability of the system.
The Lax pair for the one-dimensional Hubbard spin chain with open boundary conditions (BC) is explicitly constructed and two different kinds of boundary K-matrices compatible with the integrability of the model are obtained. Our construction provides an alternative and direct demonstration for the quantum integrability of the model and it is found that the model is related to a class of commuting transfer matrices of an equivalent coupled asymmetric six-vertex model with open BC. Our results show that the chemical potential term is indeed nontrivial for the underlying algebraic structure of the model.
Abstract Based on the Lax pair formulation, we study the integrable conditions of the Osp(1∣2) spin chain with open boundaries. We consider both the non-graded and graded versions of the Osp(1∣2) chain. The Lax pair operators M ± for the boundaries can be induced by the Lax operator M j for the bulk of the system. They correspond to the reflection equations (RE) and the Yang–Baxter equation, respectively. We further calculate the boundary K-matrices for both the non-graded and graded versions of the model with open boundaries. The double row monodromy matrix and transfer matrix of the spin chain have also been constructed. The K-matrices obtained from the Lax pair formulation are consistent with those from Sklyanin’s RE. This construction is another way to prove the quantum integrability of the Osp(1∣2) chain. We find that the Lax pair formulation has advantages in dealing with the boundary terms of the supersymmetric model.