Current jumps in flat band ladders with Dzyaloshinskii-Moriya interactions

TL;DR

This paper investigates how Dzyaloshinskii-Moriya interactions affect localized magnons and spin currents in a one-dimensional frustrated antiferromagnet, revealing distinct regimes and phenomena related to flat bands.

Contribution

It provides a detailed analysis of the impact of DM interactions on flat band systems using both analytical and numerical methods, highlighting new regimes and behaviors.

Findings

Identification of three regimes of spin current behavior.

Discovery of a jump in spin current at D=0 due to flat bands.

Demonstration of DM interactions altering ground state properties.

Abstract

Localized magnons states, due to flat bands in the spectrum, is an intensely studied phenomenon and can be found in many frustrated magnets of different spatial dimensionality. The presence of Dzyaloshinskii-Moriya (DM) interactions may change radically the behavior in such systems. In this context, we study a paradigmatic example of a one-dimensional frustrated antiferromagnet, the sawtooth chain in the presence of DM interactions. Using both path integrals methods and numerical Density Matrix Renormalization Group, we revisit the physics of localized magnons and determine the consequences of the DM interaction on the ground state. We have studied the spin current behavior, finding three different regimes. First, a Luttinger-liquid regime where the spin current shows a step behavior as a function of parameter $D$, at a low magnetic field. Increasing the magnetic field, the system is in the Meissner phase at the $m = 1/2$ plateau, where the spin current is proportional to the DM parameter. Finally, further increasing the magnetic field and for finite $D$ there is a small stiffness regime where the spin current shows, at fixed magnetization, a jump to large values at $D = 0$, a phenomenon also due to the flat band.