Solution of the modified Anderson chain

A modified Anderson lattice is proposed, whose Hamiltonian takes into account both the direct exchange interaction between band and localized electrons and their hybridization. The proposed approach allows us to take into account the dynamic processes caused by the motion of band electrons. It is shown that the ground state of the modified Anderson lattice is due to the formation of local singlets (from band and localized electrons) during the motion of band electrons along the chain and their scattering. The charge gap in the Kondo insulator is calculated for an arbitrary value of the coupling; its value is determined by the effective antiferromagnetic exchange interaction, taking into account both direct and through hybridization exchange interactions. It is shown that in the case of weak coupling the width of the gap is determined by the scattering of band electrons. Its magnitude is proportional to the squared effective exchange interaction between band and localized electrons, and in the case of a strong coupling it is determined by energy of singlet.