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

TL;DR

The paper addresses the ground-state phase diagram of a $(1/2,1/2,1)$ mixed diamond chain with a single-site anisotropy $D$ on the $\tau^{(2)}$-sites. It combines numerical (ED and DMRG) and analytical limiting-case analyses, including a large-$\lambda$ mapping to an effective XXZ chain, to reveal Néel, nonmagnetic TLL, and ferrimagnetic (QF and PF) phases, with a notable anisotropy-inversion region on the $S=1$ sublattice where $D>0$ favors Ising-like Néel and $D<0$ favors XY-like TLL. The results advance understanding of frustration- and anisotropy-driven phase competition in low-dimensional quantum magnets and connect to similar inversion phenomena in $S=1/2$ systems. The work provides a framework for exploring broader anisotropy regimes and exchange anisotropies in mixed diamond chains, with potential relevance to related materials and theoretical models.

Abstract

The ground-state phases of mixed diamond chains with ($S, τ^{(1)}, τ^{(2)})=(1/2,1/2,1)$, where $S$ is the magnitude of vertex spins, and $τ^{(1)}$ and $τ^{(2)}$ are those of apical spins, are investigated with the single-site anisotropy $D$ on the $τ^{(2)}$-site. The two apical spins in each unit cell are coupled by an exchange coupling $λ$. The vertex spins are coupled with the top and bottom apical spins by exchange couplings $1+δ$ and $1-δ$, 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 Néel ordered phase, a nonmagnetic Tomonaga-Luttinger liquid phase, quantized and partial ferrimagnetic phases. A region with anisotropy inversion is found where the Ising-like Néel 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.

Figures (5)

• Figure 1: Structure of the diamond chain investigated in this work.
• Figure 2: Ground-state phase diagrams based on the NED data with $D=1$ for (a)$L=4$, (b)$L=6$, and (c) $L=8$. The number indicated for each phase is ${M_{\rm sp}^z}$ of the ground state.
• Figure 3: Maximum value of spontaneous magnetization $m^z_{\rm sp:max}$ within the PF phase plotted against $1/L$ for $D=1$.
• Figure 4: Minimum value of $1+\delta$ and $\lambda$ plotted against $1/L$ in the narrow Néel phase for $D=1$.
• Figure 5: Ground-state phase diagrams based on the NED data with $D=-1$ for (a) $L=4$, (b) $L=6$, and (c) $L=8$. The number indicated for each phase is ${M_{\rm sp}^z}$ of the ground state. The double circles at $\lambda=0.9$ in (c) are the boundary of the nonmagnetic phase estimated from the DMRG calculation for $L=48$.