Ground states with cluster structures in a frustrated Heisenberg chain

TL;DR

This paper investigates the ground states of a frustrated Heisenberg chain with arbitrary spin, revealing phase transitions and cluster formations, including a proven four-spin cluster phase for all spins and detailed phase boundaries for spin-1/2.

Contribution

It proves the existence of a four-spin cluster phase for arbitrary spin S, extending previous numerical findings for the S=1/2 case, and characterizes phase boundaries.

Findings

Existence of a four-spin cluster phase for all spins S.

Identification of three ground state phases for S=1/2.

Determination of phase boundaries for S=1/2.

Abstract

We examine the ground state of a Heisenberg model with arbitrary spin S on a one-dimensional lattice composed of diamond-shaped units. A unit includes two types of antiferromagnetic exchange interactions which frustrate each other. The system undergoes phase changes when the ratio $\lambda$ between the exchange parameters varies. In some phases, strong frustration leads to larger local structures or clusters of spins than a dimer. We prove for arbitrary S that there exists a phase with four-spin cluster states, which was previously found numerically for a special value of $\lambda$ in the S=1/2 case. For S=1/2 we show that there are three ground state phases and determine their boundaries.