Cancellation of oscillatory behaviors in incommensurate region

TL;DR

This paper demonstrates the elimination of oscillatory behaviors in incommensurate regions of a frustrated spin system, revealing how boundary conditions and higher order corrections influence these phenomena.

Contribution

It shows that main oscillations proportional to free edge spins are eliminated in the incommensurate subphase and that higher order corrections decay exponentially.

Findings

Oscillatory behavior is eliminated in the incommensurate subphase.

π-mode oscillation is removed in the commensurate subphase.

Higher order corrections decay exponentially.

Abstract

In several frustrating systems incommensurate behaviors are often observed. For the S=1 bilinear-biquadratic model, we show that the main oscillatory behavior, which is proportional to the free edge spins, is eliminated in the incommensurate subphase, considering the average of triplet and singlet energy spectra under open boundary conditions. In the same way, the $\pi$-mode oscillation is also removed in the commensurate subphase. Moreover, we find that higher order corrections are exponentially decaying from an analysis of small size data.