Mapping between multichannel exchange models.

Abstract

We establish a mapping between different multichannel exchange models with electron spin s, impurity spin S, and channel number ${\mathit{N}}_{\mathit{f}}$. To construct the mapping we use three different techniques leading to the same results: conformal field theory, 1/${\mathit{N}}_{\mathit{f}}$ expansion, and 1/s expansion. According to our calculations two models with ${\mathit{N}}_{\mathit{f}}$ and ${\mathit{N}}_{\mathit{f}}^{\mathrm{*}}$ channels of spin s and ${\mathit{s}}^{\mathrm{*}}$ electrons, respectively, coupled to an impurity spin S should show similar low-energy properties provided the following relation holds: ${\mathit{N}}_{\mathit{fs}}$(s+1)(2s+1)=${\mathit{N}}_{\mathit{f}}^{\mathrm{*}}$${\mathit{s}}^{\mathrm{*}}$(${\mathit{s}}^{\mathrm{*}}$+1)(2${\mathit{s}}^{\mathrm{*}}$+1), irrespective of the special value of the impurity spin. This mapping seems, however, not to be consistent with the simple fusing picture used in the Bethe Ansatz solution of the multichannel problems. \textcopyright{} 1996 The American Physical Society.