R-matrix for the XX spin chain in a staggered magnetic field
P. N. Bibikov
TL;DR
This paper introduces an elliptic R-matrix for the XX spin chain in a staggered magnetic field, providing evidence for its integrability through the Yang-Baxter equation in special cases.
Contribution
It presents a new elliptic R-matrix for the XX spin chain with a staggered magnetic field, extending previous models and analyzing its integrability.
Findings
R-matrix constructed for the model
Yang-Baxter equation verified in special cases
Evidence supports integrability of the model
Abstract
We suggest the elliptic R-matrix for the XX spin chain in a staggered magnetic field. This integrable model is a special case of the more general one, studied long ago within the alternative approach by V. M. Kontorovich and V. M. Tsukernik. The Yang-Baxter equation is verified with the full rigorous only in the two special degenerate trigonometric cases. For the general one, studying the first terms of the Taylor expansions for the -matrix entries, we give the strong evidence for implementation of the Yang-Baxter equation.
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Taxonomy
TopicsMatrix Theory and Algorithms · Theoretical and Computational Physics