Rigged strings and quasimomenta in Bethe Ansatz

Heisenberg model and rigged configurations

“…The solutions 2, 11, 16 in Table 6.2 with four 1-strings and one 2-string are of the form (33). The solutions 52, 57, 72, 79 in Table 6.4 with two 1-strings and one 4-string are of the form (34). The solution 89 in Table 6.6 with one 6-string and the solution 105 in Table 6.8 with one 1-string, one 2-string and one 3-string are of the form (35).…”

Magnetic Pentagonal Ring - Galois Extensions and Crystallography

“…(8) and (9). The first class ∆ 1 gives the direct product, which is not consistent with the Galois symmetry of the Bethe number field B, whereas the second class {∆ 2 , ∆ 3 , ∆ 4 }, yields three isomorphic groups, and the first of them, of which, ∆ 2 , realizes the Galois automorphisms of B, consistent with our choice of radicals ω, γ 1 , γ −1 generating B.…”

“…(5), p denotes the pseudomomentum, and λ -the spectral parameter of a Bethe pseudoparticle. Each row in Table I contains a state of the highest weight for the pentagonal magnet, parametrized by rigged string configurations νL, with ν being the partition of r = r = 2 and denoting the string configuration, while L describes the unique collection of riggings [9,10]. It follows that all roots of Eq (4) for the interior {k = ±1, ±2} of the Brillouin zone of pentagon span the number field B/Q(ω), which is a linear space over the cyclotomic field Q(ω), of dimension four, with the basis (1, γ 1 , γ −1 , γ 1 γ −1 ), where…”

Galois Properties of the Eigenproblem of the Hexagonal Magnetic Heisenberg Ring

“…Equations (10,11) point out that all subspaces relevant in the diagonalization are either one-or two--dimensional. Clearly, projection operators P …”