English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Recently, the XXX spin chain with arbitrary boundary fields was successfullysolved [1] via the off-diagonal Bethe ansatz method [2]. The correctness andthe completeness of this solution were numerically verified by Nepomechie forone choice of the parameterizations [3]. In this paper, we discuss further thecompleteness of another parameterization of the Bethe ansatz equations and itsreduction to the parallel boundary field case. The numerical results show thatwhen the relative angle between the boundary fields turns to zero, both the T-Qrelations and the Bethe ansatz equations are reduced to the ones obtained bythe conventional Bethe ansatz methods. This allows us to establish a one-to-onecorrespondence between the Bethe roots of the unparallel boundary field caseand those of the parallel boundary field case. In the thermodynamic limit,those two sets of Bethe roots tend to the same and the contribution of therelative angle to the energy is in the order of 1/N.

Completeness and Bethe root distribution of the spin-1/2 Heisenberg chain with arbitrary boundary fields