Anomalies of kagome antiferromagnets on magnetization plateaus

TL;DR

This paper investigates the ground-state degeneracy of spin-1/2 kagome antiferromagnets on magnetization plateaus using flux insertion and anomaly arguments, revealing conditions for unique gapped ground states at specific magnetizations.

Contribution

It introduces a novel anomaly-based framework to analyze ground-state degeneracy and explains the existence of a unique gapped ground state at the 1/3 plateau.

Findings

Ground-state degeneracy bounds at specific magnetization plateaus.

Anomaly interpretation of the 1/3 plateau.

Kagome antiferromagnet can have a unique gapped ground state at 1/3 plateau due to symmetry breaking.

Abstract

We discuss the ground-state degeneracy of spin-$1/2$ kagome-lattice quantum antiferromagnets on magnetization plateaus by employing two complementary methods: the adiabatic flux insertion in closed boundary conditions and a 't Hooft anomaly argument on inherent symmetries in a quasi-one-dimensional limit. The flux insertion with a tilted boundary condition restricts the lower bound of the ground-state degeneracy on $1/9$, $1/3$, $5/9$, and $7/9$ magnetization plateaus under the $\mathrm{U(1)}$ spin-rotation and the translation symmetries: $3$, $1$, $3$, and $3$, respectively. This result motivates us further to develop an anomaly interpretation of the $1/3$ plateau. Taking advantage of the insensitivity of anomalies to spatial anisotropies, we examine the existence of the unique gapped ground state on the $1/3$ plateau from a quasi-one-dimensional viewpoint. In the quasi-one-dimensional limit, kagome antiferromagnets are reduced to weakly coupled three-leg spin tubes. Here, we point out the following anomaly description of the $1/3$ plateau. While a simple $S=1/2$ three-leg spin tube cannot have the unique gapped ground state on the $1/3$ plateau because of an anomaly between a $\mathbb Z_3\times \mathbb Z_3$ symmetry and the translation symmetry at the $1/3$ filling, the kagome antiferromagnet breaks explicitly one of the $\mathbb Z_3$ symmetries related to a $\mathbb Z_3$ cyclic transformation of spins in the unit cell. Hence the kagome antiferromagnet can have the unique gapped ground state on the $1/3$ plateau.