Ground-State Phase Diagram of (1/2,1/2,1) Mixed Diamond Chains with Single-Site Anisotropy

The ground-state phases of mixed diamond chains with ($S, \tau^{(1)}, \tau^{(2)})=(1/2,1/2,1)$, where $S$ is the magnitude of vertex spins, and $\tau^{(1)}$ and $\tau^{(2)}$ are those of apical spins, are investigated with the single-site anisotropy $D$ on the $\tau^{(2)}$-site. The two apical spins in each unit cell are coupled by an exchange coupling $\lambda$. The vertex spins are coupled with the top and bottom apical spins by exchange couplings $1+\delta$ and $1-\delta$, respectively. The ground-state phase diagram is determined using the numerical exact diagonalization and DMRG method in addition to the analytical approximations in various limiting cases. The phase diagram consists of a N\'eel ordered phase, a nonmagnetic Tomonaga-Luttinger liquid phase, and quantized and partial ferrimagnetic phases. A region with anisotropy inversion is found where the Ising-like N\'eel phase is realized for the easy-plane anisotropy $D >0$ and the XY-like Tomonaga-Luttinger liquid phase is realized for the easy-axis anisotropy $D <0$ on the $S=1$ sites.