Anisotropic pyrochlores and the global phase diagram of the checkerboard antiferromagnet

TL;DR

This paper investigates the phase diagram of anisotropic pyrochlore antiferromagnets, revealing a crossed dimer state in certain limits and proposing candidate global phase diagrams using advanced theoretical techniques.

Contribution

It introduces a combined renormalization group and bosonization approach to analyze anisotropic pyrochlore models and predicts a crossed dimer phase and possible quantum phase transitions.

Findings

Identification of a crossed dimer state in the anisotropic limit

Qualitative agreement with plaquette valence bond solid at J_ imes/J=1

Prediction of a crossed dimer state in the 3D pyrochlore model

Abstract

We study the phase diagram of two models of spin-1/2 antiferromagnets composed of corner-sharing tetrahedra, the basis of the pyrochlore structure. Primarily, we focus on the Heisenberg antiferromaget on the checkerboard lattice (also called the planar pyrochlore and crossed-chains model). This model has an anisotropic limit, when the dimensionless ratio of two exchange constants, J_\times/J << 1, in which it consists of one-dimensional spin chains coupled weakly together in a frustrated fashion. Using recently developed techniques combining renormalization group ideas and one-dimensional bosonization and current algebra methods, we show that in this limit the model enters a crossed dimer state with two-fold spontaneous symmetry breaking but no magnetic order. We complement this result by an approximate ``quadrumer triplet boson'' calculation, which qualitatively captures the physics of the ``plaquette valence bond solid'' state believed to obtain for J_\times/J = 1. Using these known points in parameter space, the instabilities pointed to by the quadrumer boson calculation, and the simple limit J_\times/J >> 1, we construct a few candidate global phase diagrams for the model, and discuss the nature of the quantum phase transitions contained therein. Finally, we apply our quasi-one-dimensional techniques to an anisotropic limit of the three-dimensional pyrochlore antiferromagnet, an approximate model for magnetism in GeCu2O4. A crossed dimer state is predicted here as well.