In the present paper, we study the quantum phase transition in the mixed-spin Heisenberg model with the single-ion anisotropy on a bipartite lattice. We prove rigorously that, when the single-ion anisotropy energy
D is positive, the model has a unique ground state with the total spin-
z component
Sz=0. On the other hand, when the single-ion anisotropy energy is negative and favors the longitudinal spin direction, the global ground state of the system becomes doubly degenerate. Therefore,
D=0 is the bifurcation point for the global ground state of the system. Furthermore, we show also that, in the latter case, the global ground state of the mixed-spin Heisenberg chain has the ferrimagnetic long-range order. Our conclusions confirm and generalize the previous results derived by numerical calculations on small size samples.
The ground-state properties of the spin-(1/2, 1) mixed-spin XXZ chain with single-ion anisotropy (D) are investigated by the infinite time-evolving block decimation (iTEBD) method. A ground-state phase diagram including three phases, i.e., a fully polarized phase, an XY phase and a ferrimagnetic phase, is obtained. The ferrimagnetic phase is found to extend to the regions with (Δ > 1, D > 0) and (Δ < 1, D < 0), where Δ denotes the coupling anisotropy between the localized spins. By the discontinuous behavior of bipartite entanglement, quantum phase transitions (QPTs) between the XY phase and the other two phases are verified to be of the first-order. Furthermore, two constant spontaneous magnetization values (M z = 3/2 and 1/2) are observed in the fully polarized and the ferrimagnetic phases, respectively. In both cases of Δ → +∞ and D → -∞, the ground state tends to the Ising limit. In addition, both the long-range ferromagnetic and antiferromagnetic orders are found to coexist in the whole ferrimagnetic phase.
The linear real space renormalization group is applied to study alternating spin (1/2,1) chains. The temperature dependences of the specific heat and spin–spin correlation functions for the quantum easy-axis mixed-spin chain are found. The role of single-ion anisotropy is discussed. The phase diagram of Ising spin chains with antiferromagnetic intrachain interactions and weak ferromagnetic interchain interactions is presented. As one expects, the weak interchain coupling leads to antiferrimagnetic long-range order in several chains. The threshold value of single-ion anisotropy below which the system does not exhibit a phase transition is found.