Elementary excitations in the gapped phase of a frustrated S=1/2 spin ladder: from spinons to the Haldane triplet

TL;DR

This study investigates elementary excitations in a frustrated S=1/2 spin ladder, revealing a transition from free spinons to confined triplet excitations, using variational matrix-product states and comparing with exact diagonalization.

Contribution

It introduces a variational matrix-product ansatz to analyze elementary excitations in a frustrated S=1/2 ladder with alternating exchange, capturing the confinement transition of spinons.

Findings

Spinons are free in the uniform ladder

Alternation confines spinons into S=1 triplets

Qualitative agreement with exact diagonalization data

Abstract

We use the variational matrix-product ansatz to study elementary excitations in the S=1/2 ladder with additional diagonal coupling, equivalent to a single S=1/2 chain with alternating exchange and next-nearest neighbor interaction. In absence of alternation the elementary excitation consists of two free S=1/2 particles ("spinons") which are solitons in the dimer order. When the nearest-neighbor exchange alternates, the "spinons" are confined into one S=1 excitation being a soliton in the generalized string order. Variational results are found to be in a qualitative agreement with the exact diagonalization data for 24 spins. We argue that such an approach gives a reasonably good description in a wide range of the model parameters.