arXiv:1307.0280 · Nuclear Physics B

Spin- 12 XYZ model revisit: General solutions via off-diagonal Bethe ansatz

Junpeng Cao, Shuai Cui, Wen‐Li Yang, Kangjie Shi, Yupeng Wang

Published Jul 3, 2014• 60 citations

Abstract

The spin-12 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the inhomogeneous T–Q relations, which allow us to treat both the even N (the number of lattice sites) and odd N cases simultaneously in a unified approach.

DOI: 10.1016/j.nuclphysb.2014.06.026

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arXiv:1307.0280 · Nuclear Physics B

Spin- 12 XYZ model revisit: General solutions via off-diagonal Bethe ansatz

Junpeng Cao, Shuai Cui, Wen‐Li Yang, Kangjie Shi, Yupeng Wang

Published Jul 3, 2014• 60 citations

arXiv HTML PDF

Abstract

DOI: 10.1016/j.nuclphysb.2014.06.026

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Off-diagonal Bethe Ansatz for the

{D}_3^{(1)}

model

Abstract The exact solutions of the

{D}_3^{(1)}

D 3 1 model (or the so(6) quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator product identities are obtained, which are sufficient to enable us to determine spectrum of the system. Eigenvalues of the fused transfer matrices are constructed by the T - Q relations for the periodic case and by the inhomogeneous T- Q one for the non-diagonal boundary reflection case. The present method can be generalized to deal with the

{D}_n^{(1)}

D n 1 model directly.

Off-diagonal Bethe Ansatz solution of the

τ_2

-model

The generic quantum

τ_2

-model (also known as Baxter-Bazhanov-Stroganov (BBS) model) with periodic boundary condition is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix (solutions of the recursive functional relations in

τ_j

-hierarchy) with generic site-dependent inhomogeneity parameters are given in terms of an inhomogeneous T-Q relation with polynomial Q-functions. The associated Bethe Ansatz equations are obtained. Numerical solutions of the Bethe Ansatz equations for small number of sites indicate that the inhomogeneous T-Q relation does indeed give the complete spectrum.