Anharmonic Ground state selection in the pyrochlore antiferromagnet

TL;DR

This paper investigates how anharmonic quantum fluctuations lift degeneracies in the pyrochlore antiferromagnet, revealing a near-degenerate family of states influenced by loop structures, extending previous harmonic analyses.

Contribution

It extends spin-wave calculations to quartic order, demonstrating how anharmonic effects partially lift classical degeneracy in the pyrochlore antiferromagnet.

Findings

Quartic order breaks harmonic degeneracy of ground states.

Effective Hamiltonian depends on loop structures, especially loops of length 26.

Pyrochlore exhibits unique anharmonic behavior compared to kagome and checkerboard lattices.

Abstract

In the pyrochlore lattice Heisenberg antiferromagnet, for large spin length $S$, the massive classical ground state degeneracy is partly lifted by the zero-point energy of quantum fluctuations at harmonic order in spin-waves. However, there remains an infinite manifold of degenerate collinear ground states, related by a gaugelike symmetry. We have extended the spin-wave calculation to quartic order, assuming a Gaussian variational wavefunction (equivalent to Hartree-Fock approximation). Quartic calculations \emph{do} break the harmonic-order degeneracy of periodic ground states. The form of the effective Hamiltonian describing this splitting, which depends on loops, was fitted numerically and also rationalized analytically. We find a family of states that are still almost degenerate, being split by the term from loops of length 26. We also calculated the anharmonic terms for the checkerboard lattice, and discuss why it (as well as the kagom\'e lattice) behave differently than the pyrochlore at anharmonic orders.