Asymmetric Anderson model and spin excitations in the Kondo insulator YbB12

A cluster problem is analyzed as an example demonstrating that the observed three-mode behavior of spin-triplet excitations in YbB₁₂ can be described by the asymmetric Anderson model with insulating singlet ground state. In the case of an infinite system, it is argued that the behavior of the f subsystem can be analyzed by using an effective Hamiltonian ? _J with direct antiferromagnetic f-f exchange interaction. The spin excitation spectrum is shown to have a minimum at the antiferromagnetic vector, as observed experimentally. A distinctive feature of the analysis is the use of singlet and triplet basis operators.