The planar pyrochlore antiferromagnet: A large-N analysis

TL;DR

This paper investigates the quantum phases of the Heisenberg antiferromagnet on the planar pyrochlore lattice using a large-N approach, revealing a $Z_2$ spin-liquid phase and other ordered phases.

Contribution

It provides a large-N analysis of the phase diagram for the planar pyrochlore antiferromagnet, identifying potential quantum disordered and ordered phases.

Findings

Discovery of a $Z_2$ spin-liquid phase in a narrow parameter region

Identification of plaquette-ordered and staggered spin-Peierls phases

Analysis of fluctuation effects around the large-N limit

Abstract

We study possible quantum phases of the Heisenberg antiferromagnet on the planar pyrochlore lattice, also known as the checkerboard lattice or the square lattice with crossings. It is assumed that the exchange coupling on the square-lattice-links is not necessarily the same as those along the crossing links. When all the couplings are the same, this model may be regarded as a two dimensional analog of the pyrochlore antiferromagnet. The large-N limit of the Sp($N$) generalized model is considered and the phase diagram is obtained by analyzing the fluctuation effects about the $N \to \infty$ limit. We find a topologically-ordered $Z_2$-spin-liquid phase in a narrow region of the phase diagram as well as the plaquette-ordered and staggered spin-Peierls phases as possible quantum-disordered paramagnetic phases.