Quantum entanglement and quantum phase transition of the spin-1 Heisenberg chain with single-ion anisotropy

Quantum entanglement and quantum phase transition of the spin-1 Heisenberg chain with single-ion anisotropy have been investigated by using the quantum renormalization group method. It is found that the quantum entanglement of the system tends to different saturated values and exhibits perfect step-like plateaus in each phase separated by the critical points, as well as abrupt drop emerged at the quantum critical points as the size of the system increases. The single-ion anisotropy parameter suppresses the entanglement due to favoring the alignment of spins and influences the quantum phase transition of the system. The first partial derivative of the entanglement with respect to the single-ion anisotropy parameter exhibits a nonanalytic or maximum behavior at the critical points, which directly associates with the divergence of the correlation length. Furthermore, the entanglement critical exponents and the correlation length exponents have been obtained, which shows the scaling behaviors of the spin system. This work has extended the application of entanglement for depicting the quantum phase transition and its significant properties in spin-1 systems.