Anharmonic Ground state selection in the pyrochlore antiferromagnet

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 kagomé lattice) behave differently than the pyrochlore at anharmonic orders.

24 pp, 10 figures. Part of Sec. V D moved to be new App. B; elaborated intro. of Sec. VI

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• Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions
• Thermodynamics of the pyrochlore Heisenberg ferromagnet with arbitrary spin $S$
• Mott-Hubbard transition and spin-liquid state on the pyrochlore lattice
• Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism
• Color ice states, weathervane modes, and order by disorder in the bilinear-biquadratic pyrochlore Heisenberg antiferromagnet
• Competing orders in a frustrated Heisenberg model on the Fisher lattice
• Goldstone modes in the emergent gauge fields of a frustrated magnet
• Schwinger boson mean field perspective on emergent spins in diluted Heisenberg antiferromagnets
• Decision making by Berry's flux