Opening of the Haldane Gap in Anisotropic Two- and Four-Leg Spin Ladders

TL;DR

This paper investigates how the Haldane gap opens in anisotropic two-leg and four-leg spin ladders, revealing distinct behaviors and phase diagrams for each case using bosonization and renormalization group techniques.

Contribution

It provides a detailed analysis of the phase diagram and the conditions for the Haldane gap opening in two- and four-leg spin ladders, highlighting differences due to anisotropy and coupling.

Findings

Haldane gap opens for any small interchain coupling in two-leg ladders.

Haldane phase exists over a large parameter space in two-leg ladders.

In four-leg ladders, the Haldane gap depends on coupling and anisotropy, existing only near the isotropic point.

Abstract

We study the opening of the Haldane gap in two-leg and four-leg anisotropic spin ladders using bosonization and renormalization group methods, and we determine the phase diagram as a function of the interchain coupling and the relative anisotropy. It is found that the opening of the Haldane gap is qualitatively different for the two cases considered. For the two-leg ladder the Haldane gap opens for arbitrarily small interchain coupling, independent of the relative anisotropy, and the Haldane phase exists in a large region of parameter space. For the four-leg ladder the opening of the Haldane gap is strongly dependent on both the interchain coupling as well as the relative anisotropy, and the Haldane phase exists only in a narrow region about the isotropic antiferromagnet.