Soft modes, Gaps and Magnetization Plateaus in 1D Spin-1/2 Antiferromagnetic Heisenberg Models

TL;DR

This paper investigates the emergence of magnetization plateaus and soft modes in one-dimensional spin-1/2 antiferromagnetic Heisenberg models with additional couplings and fields, analyzing their critical behavior and extensions to ladder systems.

Contribution

It introduces a detailed analysis of how dimer perturbations induce magnetization plateaus and relates their evolution to critical exponents, extending understanding to ladder systems.

Findings

Magnetization plateaus occur at specific fractional values of magnetization.

Plateau strength scales as a power law with the perturbation parameter.

Critical behavior is characterized by the eta-exponent related to the structure factor.

Abstract

We study the one-dimensional spin-1/2 model with nearest and next-to-nearest-neighbor couplings exposed to a homogeneous magnetic field $h_{3}$ and a dimer field with period $q$ and strength $\delta$. The latter generates a magnetization plateau at $M=(1-q/\pi)/2$, which evolves with strength $\delta$ of the perturbation as $\delta^{\epsilon}$, where $\epsilon=\epsilon(h_{3},\alpha)$ is related to the $\eta$-exponent which describes the critical behavior of the dimer structure factor, if the perturbation is switched of ($\delta=0$). We also discuss the appearance of magnetization plateaus in ladder systems with $l$ legs.