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arXiv:1307.2023 · Nuclear Physics B

Off-diagonal Bethe ansatz solutions of the anisotropic spin- 12 chains with arbitrary boundary fields

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

Published Oct 10, 2013• 123 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysb.2013.10.001

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In two previous papers [26], [27], the exact solutions of the spin-12 chains with arbitrary boundary fields were constructed via the off-diagonal Bethe ansatz (ODBA). Here we introduce a method to approach the thermodynamic limit of those models. The key point is that at a sequence of degenerate points of the crossing parameter η=ηm, the off-diagonal Bethe ansatz equations (BAEs) can be reduced to the conventional ones. This allows us to extrapolate the formulae derived from the reduced BAEs to arbitrary η case with O(N−2) corrections in the thermodynamic limit N→∞. As an example, the surface energy of the XXZ spin chain model with arbitrary boundary magnetic fields is derived exactly. This approach can be generalized to all the ODBA solvable models.
In two previous papers [26, 27], the exact solutions of the spin-1/2 chains with arbitrary boundary fields were constructed via the off-diagonal Bethe ansatz (ODBA). Here we introduce a method to approach the thermodynamic limit of those models. The key point is that at a sequence of degenerate points of the crossing parameter \eta=\eta_m, the off-diagonal Bethe ansatz equations (BAEs) can be reduced to the conventional ones. This allows us to extrapolate the formulae derived from the reduced BAEs to arbitrary \eta case with O(N^{-2}) corrections in the thermodynamic limit N\to\infty. As an example, the surface energy of the XXZ spin chain model with arbitrary boundary magnetic fields is derived exactly. This approach can be generalized to all the ODBA solvable models.
Spectrum of the quantum integrable D2(2) {D}_2^{(2)} D2(2)​ spin chain with generic boundary fields
Abstract Exact solution of the quantum integrable D2(2) {D}_2^{(2)} D2(2)​ D 2 2 spin chain with generic integrable boundary fields is constructed. It is found that the transfer matrix of this model can be factorized as the product of those of two open staggered anisotropic XXZ spin chains. Based on this identity, the eigenvalues and Bethe ansatz equations of the D2(2) {D}_2^{(2)} D2(2)​ D 2 2 model are derived via off-diagonal Bethe ansatz.