Macroscopic degeneracy of ground state in the frustrated Heisenberg diamond chain

TL;DR

This paper investigates the frustrated Heisenberg diamond chain, revealing a macroscopically degenerate ground state with localized magnons and flat bands, leading to high residual entropy and novel magnetic properties.

Contribution

It demonstrates the exact macroscopic degeneracy of the ground state and the presence of localized magnon states in the frustrated Heisenberg diamond chain.

Findings

Ground state degeneracy is 4^n for n diamonds.

Existence of flat bands in one-, two-, and three-magnon spectra.

High residual entropy per spin, s_0 = (2/3) ln 2.

Abstract

The spin-$\frac{1}{2}$ Heisenberg diamond chain with ferro- and antiferromagnetic exchange interactions is studied. The phase boundary in the parametric space of these interactions is determined, where the transition between the ferromagnetic and other (singlet or ferrimagnetic) ground state phases occurs. On this phase boundary there is a dispersionless (flat) energy band in the one-magnon spectrum and these states can be represented as localized magnons in the trapping cells between neighboring diamonds. The ground state consists of the localized magnons and special magnon complexes and it is macroscopically degenerate. A remarkable feature of the model is the existence, on a certain part of the phase boundary, of two- and three-magnon localized states, forming flat bands in two- and three-magnon spectrum. All these localized states also belong to the ground state manifold, which turns out to be exactly the same as for the system of independent spins-$\frac{3}{2}$. This implies a large macroscopic degeneracy of the ground state $4^n$ ($n$ is number of diamonds in the chain) and a high residual entropy per spin $s_{0}=\frac{2}{3}\ln 2$.