Stable particles in anisotropic spin-1 chains

TL;DR

This paper investigates stable excitations in anisotropic spin-1 chains, confirming some theoretical predictions with numerical data and revealing complex behavior in different phases.

Contribution

It provides a detailed numerical and theoretical analysis of stable particles and breathers in anisotropic spin-1 chains, highlighting phase-dependent differences.

Findings

Stable breathers near phase boundary in large-D phase

No stable breathers observed in Haldane phase

Identification of three modes via anisotropic Non-Linear Sigma Model

Abstract

Motivated by field-theoretic predictions we investigate the stable excitations that exist in two characteristic gapped phases of a spin-1 model with Ising-like and single-ion anisotropies. The sine-Gordon theory indicates a region close to the phase boundary where a stable breather exists besides the stable particles, that form the Haldane triplet at the Heisenberg isotropic point. The numerical data, obtained by means of the Density Matrix Renormalization Group, confirm this picture in the so-called large-D phase for which we give also a quantitative analysis of the bound states using standard perturbation theory. However, the situation turns out to be considerably more intricate in the Haldane phase where, to the best of our data, we do not observe stable breathers contrarily to what could be expected from the sine-Gordon model, but rather only the three modes predicted by a novel anisotropic extension of the Non-Linear Sigma Model studied here by means of a saddle-point approximation.