Magnetization plateau and quantum phase transition of the S=1/2 trimerized XXZ spin chain

TL;DR

This paper investigates the magnetization plateau at one-third saturation in an S=1/2 trimerized XXZ spin chain, identifying a Berezinskii-Kosterlitz-Thouless quantum phase transition through numerical analysis.

Contribution

It precisely determines the phase boundary between plateau and no-plateau states in the parameter space of anisotropy and trimerization.

Findings

Identified the phase boundary between plateau and no-plateau states.

Confirmed the transition is of the Berezinskii-Kosterlitz-Thouless type.

Mapped the phase diagram in the $ riangle$-$t$ plane.

Abstract

We study the plateau of the magnetization curve at $M = M_{\rm s}/3$ ($M_{\rm s}$ is the saturation magnetization) of the $S=1/2$ trimerized $XXZ$ spin chain. By examining the level crossing of low-lying excitations obtained from the numerical diagonalization, we precisely determine the phase boundary between the plateau state and the no-plateau state on the $\Delta-t$ plane, where $\Delta$ denotes the $XXZ$ anisotropy and $t$ the magnitude of the trimerization. This quantum phase transition is of the Berezinskii-Kosterlitz-Thouless type.