Two-dimensional spin models with macroscopic degeneracy

TL;DR

This paper investigates anisotropic two-dimensional spin-1/2 models on Tasaki and kagome lattices, revealing macroscopic ground state degeneracy mainly due to bound magnon complexes, with implications for residual entropy and magnetic properties.

Contribution

It introduces an exact wave function approach to estimate ground state degeneracy in complex spin models, highlighting the role of bound magnon complexes.

Findings

Ground state degeneracy is exponentially large.

Bound magnon complexes dominate residual entropy.

The approach accurately estimates the number of ground states.

Abstract

We consider a class of anisotropic spin-$\frac{1}{2}$ models with competing ferro- and antiferromagnetic interactions on two-dimensional Tasaki and kagome lattices consisting of corner sharing triangles. For certain values of the interactions the ground state is macroscopically degenerated in zero magnetic field. In this case the ground state manifold consists of isolated magnons as well as the bound magnon complexes. The ground state degeneracy is estimated using a special form of exact wave function which admits arrow configuration representation on two-dimensional lattice. The comparison of this estimate with the result for some special exactly solved models shows that the used approach determines the number of the ground states with exponential accuracy. It is shown that the main contribution to the ground state degeneracy and the residual entropy is given by the bound magnon complexes.