‘Bethe-ansatz-free’ eigenstates for spin-1/2 Richardson–Gaudin integrable models
نویسندگان
چکیده
In this work we construct the eigenstates of most general spin-1/2 Richardson-Gaudin model integrable in an external magnetic field. This includes possibility for fully anisotropic XYZ coupling such that $S^x_iS^x_j$, $S^y_iS^y_j$ and $S^z_iS^z_j$ terms all have distinct strengths. While insuring integrability is maintained presence field excludes elliptic which only at zero field, still covers a wide class (XYZ) models associated with non skew-symmetric r-matrices. The eigenstates, as constructed here, do not require any usable Bethe ansatz therefore: no proper pseudo-vacuum, roots, or generalised spin raising (Gaudin) operators to be defined. Indeed, are generically built through conserved charges define interest specification set eigenvalues defining particular eigenstate. Since these are, general, solutions simple quadratic equations, proposed approach simpler implement than and, moreover, it remains completely identical independently symmetries model. construction removes distinction between XXZ/XXX generically, without U(1) so difficulties use cases avoided.
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ژورنال
عنوان ژورنال: Journal of Physics A
سال: 2022
ISSN: ['1751-8113', '1751-8121']
DOI: https://doi.org/10.1088/1751-8121/ac92ac