The S=1 quantum spin chain with equal Heisenberg and biquadratic exchange was shown by Sutherland to be integrable. In this paper the equations obtained by Sutherland are solved numerically to obtain the behaviour at zero temperature in a magnetic field. It is found that there is an additional phase change at a lower field than the spin flop field. This new phase change marks the boundary between a regime in which the ground state contains only atoms with S z =1, 0 and one in which 1, 0 and -1 are present. The form of the elementary excitations in the two regimes is discussed and the possibility of a similar phase change in the pure Heisenberg model is considered.
We generalize the iterative diagonalization procedure adopted in the method of numerical renormalization group to analyze the Kondo effect in strong magnetic fields, where the density of states for itinerary electrons at the chemical potential varies discontinuously as the magnetic field changes. We first examine phases of many-body ground states in the presence of a single impurity. By investigating the change of the
z component of total spin, $\mathrm{\ensuremath{\Delta}}{S}_{z}$, and spin-spin correlation between the impurity and conduction electrons, we find that there are three states competing for the ground state when Zeeman splitting is present. One of the states is a doublet in which the impurity spin is unscreened. The other two states are Kondo screening states with $\mathrm{\ensuremath{\Delta}}{S}_{z}=\frac{1}{2}$ and 1, in which the impurity spin is partially screened and completely screened, respectively. For Kondo systems with two impurities in strong magnetic fields, we find that the interplay between the Kondo screening effect, Rudermann-Kittel-Kasuya-Yoshida interaction, and quantum oscillations due to Landau levels determines the ground state of the system. A combination of these three factors results in different screening scenarios for different phases in which spins of two impurities can form spin-0 or spin-1 states, while impurity spins in these phases can be either screened, partially screened, or unscreened by conduction electrons. The emergence of the ground state from these competing states oscillates with the change of magnetic field, chemical potential or inter-impurity distance. This leads to quantum oscillations in magnetization and conductivity. In particular, we find extra peak structures in longitudinal conductivity that reflect changes of Kondo screening phases and are important features to be observed in experiments. Our results provide a complete characterization of phases for Kondo effect in strong magnetic fields.
Magnetization process of ( S = 3/2, S = 1) ferrimagnetic spin chain with single-ion anisotropy D is investigated by numerical diagonalization. The magnetization process has a plateau at 1/5 of the saturation moment in the small D region. We find a quantum phase transition that the plateau once vanishes at a critical D and revives in the large D region. The critical value D c is estimated to be 0.9. In order to clarify the mechanism of this transition, we propose new trial states: a pentamer state in the small D phase and a trimer state in the large D phase. We find that representative ground state is changed from the pentamer state to the trimer one, while D increases across D c. This result suggests that the mechanism of the quantum phase transition is understood as the change of the representative ground state.