Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2008-11-03
Phys. Rev. B 80, 014407 (2009) [23 pp]
Physics
Condensed Matter
Strongly Correlated Electrons
24 pp, 10 figures. Part of Sec. V D moved to be new App. B; elaborated intro. of Sec. VI
Scientific paper
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.
Henley Christopher L.
Hizi Uzi
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