Quasimomenta of string configurations

Abstract

We sketch a reciprocal space analogue of the combinatorial bijection of Robinson- Schensted and Kerov-Kirillov-Reshetikhin (RSKKR) between magnetic configurations (the initial basis for quantum calculations of the eigenproblem of the Heisenberg Hamiltonian for a one-dim finite Heisenberg chain), and rigged string configurations (the classification labels for the exact results of Bethe Ansatz). Existence of such a bijection admits an interpretation of the exact quantum numbers of riggings as quasimomenta of l-strings. The extended size of an l-string results in selection rules for these quasimomenta, and thus in a division of the Brillouin zone into compact subzones of forbidden and allowed states of the system of coupled Bethe pseudoparticles. The forbidden Brillouin subzone for a particular l-string is evidently the effect of kinematical restrictions for motions of constituent Bethe pseudoparticles. These restrictions can be easily predicted in a combinatorially unique way due to completness of the RSKKR bijection.