Valence-bond theory of the Kondo lattice model in one dimension

Abstract

We present a detailed analysis of the Kondo chain model using a valence-bond formalism that has the advantage of exploiting the total spin invariance of the Kondo lattice model. The ground-state energy per site of the Kondo chain extrapolates smoothly to give an accurate infinite-chain result. The analysis of the ground-state wave function in terms of the weight of the fully quenched state indicates that the infinite system will show complete spin quenching for an infinitesimal value of the interaction strength J/t. The spin-correlation functions of finite Kondo chains support this view. The singlet-triplet gap dependence on the system size is also consistent with this picture. The lowest excited-singlet excited state shows a qualitatively different behavior from that of the ground state, leading us to conclude that, while the triplet excited state has a spinlike excitation, the excited singlet state has a chargelike excitation. Comparison of the finite Hubbard and Kondo models shows that the Hubbard model, for small interaction strengths, suppresses double occupancy of the orbitals more than the Kondo model, but for large interaction strengths the Kondo model has a lower double occupancy than the Hubbard model. An introduction of the Hubbard correlations in the conduction band of the Kondo model drives the system into a nonmagnetic state, unlike in the Hubbard model, where the system exhibits antiferromagnetic spin correlations.