Entanglement and quantum phase transition in a mixed-spin Heisenberg chain with single-ion anisotropy

We study the ground-state and thermal entanglement in the mixed-spin (S,s)=(1,1/2) Heisenberg chain with single-ion anisotropy D using exact diagonalization of small clusters. In this system, a quantum phase transition is revealed to occur at the value D=0, which is the bifurcation point for the global ground state; that is, when the single-ion anisotropy energy is positive, the ground state is unique, whereas when it is negative, the ground state becomes doubly degenerate and the system has the ferrimagnetic long-range order. Using the negativity as a measure of entanglement, we find that a pronounced dip in this quantity, taking place just at the bifurcation point, serves to signal the quantum phase transition. Moreover, we show that the single-ion anisotropy helps to improve the characteristic temperatures above which the quantum behavior disappears.