Phase diagram and macroscopic ground state degeneracy of frustrated spin-1/2 anisotropic Heisenberg model on diamond-decorated lattices

TL;DR

This work analyzes the ground-state properties of an anisotropic spin-$\tfrac{1}{2}$ Heisenberg model built from ideal diamond units with competing ferromagnetic and antiferromagnetic couplings, across one-, two-, and three-dimensional diamond-decorated lattices. The authors combine exact local-state analysis of the diamond unit with transfer-matrix and bond-percolation mappings to count degeneracies, revealing four competing phases—ferromagnetic (F), critical (C), monomer-dimer (MD), and tetramer-dimer (TD)—that meet at a quadruple point with maximal degeneracy $W=4^n$ in 1D and lattice-dependent but similarly large degeneracies in higher dimensions. They quantify degeneracies on phase boundaries: MD/F ($W=3^n$), MD/TD ($W=(12/5)^n$), and MD (inside) where $W=2^n$, with the quadruple point achieving the largest $W$; in higher dimensions the MD/TD boundary is studied via transfer-matrix and MD/F via percolation, yielding residual entropies $S_0$ that depend on lattice geometry. These results map out the rich macroscopic degeneracy landscape of frustrated F-AF diamond systems and connect ground-state counting to percolation and transfer-matrix frameworks, highlighting potential implications for low-temperature thermodynamics and magnetic cooling.

Abstract

We study the ground state properties of the anisotropic spin-1/2 Heisenberg model on lattices built from ideal diamond units with competing ferro- and antiferromagnetic interactions. The study covers the one-dimensional diamond chain and its two- and three-dimensional generalizations. The ground-state phase diagram contains four distinct phases: ferromagnetic (F), critical (C), monomer-dimer (MD), and tetramer-dimer (TD), which converge at a quadruple point. We demonstrate the presence of macroscopic ground-state degeneracy and corresponding residual entropy, which is maximal at the quadruple point and also extends throughout the MD phase and its boundaries with TD and F phases. For the diamond chain, we derive exact degeneracies, while for higher-dimensional lattices, we map the problem onto a bond percolation model or used transfer-matrix approach, enabling the numerical computation of the ground state degeneracy.

Figures (6)

• Figure 1: Ideal diamond unit described by Hamiltonian (\ref{['h']}). The solid lines denote the anisotropic ferromagnetic bonds, the dashed line represents the anisotropic antiferromagnetic diagonal bond.
• Figure 2: Ground state phase diagram for the case $J_{z}=J_{\perp }=J$. The interaction $J_0$ is taken as energy unit ($J_0=1$).
• Figure 3: Ground state phase diagram for the case $\Delta =2$. The interaction $J_0$ is taken as energy unit ($J_0=1$).
• Figure 4: Ideal diamond decorated square lattice 4x4 with particular configuration of diamonds with singlets on diagonal (shaded diagonals) and the corresponding percolation configuration with connected and disconnected bonds.
• Figure 5: The values of $G=W^{1/n}$ as a function of $1/n$ for the square, triangular, honeycomb and cubic lattices.