An S=1/2 impurity spin in the antiferromagnetic S=1 bond-alternating chain

We explore low-lying excited states as well as the ground state of the antiferromagnetic S = 1 bond-alternating chain with an S impurity spin. For the case where the ground-state phase of the host system is the Haldane phase, we review a numerical analysis of the electron-spin-resonance experimental results on the NENP:Cu2+ system. For the case where the ground-state phase of the host system is the dimer phase, on the other hand, we calculate, using the exact-diagonalization method, the dependences of the energy differences between the ground and low-lying excited states upon both the impurity-host exchange constant and the single-ion-type anisotropy constant, and also calculate, using the density-matrix renormalization-group method, the external-magnetic-field dependence of the impurity-spin magnetizaion in the ground state. In these calculations, we keep the NTENP:Cu2+ system in mind to choose the value of the bond-alternation parameter. We find that a few low-lying excited states which are expected from the valence-bond-solid picture appear as the impurity states in the energy gap between the singlet ground arid triplet first-excited states (the dimer gap). Furthermore, for certain values of the above constants, we find that the impurity-spin magnetizaion shows a clear jump at a magnetic field which is in the dimer-gap region or in the magnetization-plateau region of the host system, and also that the impurity-spin magnetizaion has a magnetic-field region where it decreases as a function of the magnetic field.