Behavior of a frustrated quantum spin chain with bond dimerization

TL;DR

This paper investigates the excitation gap behavior in a frustrated quantum spin chain with bond dimerization, revealing how the gap varies with frustration and dimerization, using numerical and variational methods.

Contribution

It provides a detailed analysis of the excitation gap and low-lying excitations in a frustrated S=1/2 quantum spin chain, including exact results on gap enhancement and localization length.

Findings

Minimum energy gap at the fully-frustrated point

Gap enhancement follows a power law with exponent 2/3

Localized kink and anti-kink govern low-lying excitations

Abstract

We clarified behavior of the excitation gap in a frustrated S=1/2 quantum spin chain with bond dimerization by using the numerical diagonalization of finite systems and a variational approach. The model interpolates between the independent dimer model and the S=1 spin chain by changing a strength of the dimerization. The energy gap is minimum at the fully-frustrated point, where a localized kink and a freely mobile anti-kink govern the low-lying excitations. Away from the point, a kink and an antikink form a bound state by an effective triangular potential between them. The consequential gap enhancement and the localization length of the bound state is obtained exactly in the continuous limit. The gap enhancement obeys a power law with exponent 2/3. The method and the obtained results are common to other frustrated double spin-chain systems, such as the one-dimensional J_1 - J_2 model, or the frustrated ladder model.