Low-lying magnon excitations in integer-spin ladders and tubes

TL;DR

This paper investigates low-energy magnon excitations in integer-spin ladder and tube systems, revealing degeneracy patterns and phase transitions under external magnetic fields using a nonlinear sigma model approach.

Contribution

It provides a unified field-theoretical analysis of both frustrated and non-frustrated systems, identifying degeneracy structures and phase behavior in low-energy excitations.

Findings

Frustrated tubes have six-fold degenerate magnon bands.

Non-frustrated systems have triply degenerate magnon bands.

Strong external fields induce phase transitions to Tomonaga-Luttinger liquids.

Abstract

We consider low-energy excitation structures of N-leg integer-spin ladder and tube systems with an antiferromagnetic (AF) intrachain coupling and a uniform external field. The tube means the ladder with the periodic boundary condition along the interchain (rung) direction. Odd-leg AF-rung tubes have the frustration. In order to analyze all systems including frustrated tubes, we apply a field-theoretical method based on the nonlinear sigma model. We mainly focus on the systems without any external fields. In this case, it is shown that the lowest bands of frustrated tubes always consist of six-fold degenerate magnon excitations, while those of all other systems are triply degenerate. This result implies that the ground states of frustrated tubes (all non-frustrated systems) become a two (one)-component Tomonaga-Luttinger liquid, when a sufficiently strong uniform field is applied.