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

TL;DR

This paper investigates the phase diagram and ground state degeneracy of a frustrated spin-1/2 anisotropic Heisenberg model on diamond-decorated lattices, revealing multiple phases and macroscopic degeneracy with exact and numerical methods.

Contribution

It provides a comprehensive analysis of the phase diagram and degeneracy in higher-dimensional diamond lattices, extending previous one-dimensional results with exact and numerical approaches.

Findings

Identified four distinct ground-state phases: ferromagnetic, critical, monomer-dimer, and tetramer-dimer.

Discovered maximal residual entropy at the quadruple point and extended degeneracy in the phase diagram.

Mapped higher-dimensional models onto percolation and transfer-matrix models to compute degeneracies.

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.