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Journal of Physics A Mathematical and General

Graded reflection equations and the one-dimensional small-polaron open chain

Huan-Qiang Zhou

Published Jan 21, 1997• 7 citations
Publisher

Abstract

The graded reflection equations are presented to describe quantum integrable lattice fermion open chains on a finite interval with independent boundary conditions on each end. Specifically, the general boundary K supermatrices are determined for the one-dimensional small-polaron open chain. The result is consistent with the system under study admitting Lax pair formulation.

DOI
10.1088/0305-4470/30/2/030

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Communications in Theoretical Physics•Sep 1, 2022•0 citations
The graded reflection equations are presented to describe quantum integrable lattice fermion open chains on a finite interval with independent boundary conditions on each end. Specifically, the general boundary K supermatrices are determined for the one-dimensional small-polaron open chain. The result is consistent with the system under study admitting Lax pair formulation.
Employing the graded versions of the Yang-Baxter equation and the reflection equations, we construct two kinds of integrable impurities for a small-polaron model with general open boundary conditions: (a) we shift the spectral parameter of the local Lax operator at arbitrary sites in the bulk and (b) we embed the impurity fermion vertex at each boundary of the chain. The Hamiltonians with different types of impurity terms are given explicitly. The Bethe ansatz equations, as well as the eigenvalues of the Hamiltonians, are constructed by means of the quantum inverse scattering method. In addition, we discuss the ground-state properties in the thermodynamic limit.
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.