Renormalized Classical Theory of Quantum Magnets

Abstract

We derive a renormalized classical spin (RCS) theory for $S>1/2$ quantum magnets by constraining a generalized classical theory that includes all multipolar fluctuations to a reduced CP${}^1$ phase space of dipolar SU($2$) coherent states. When the spin Hamiltonian ${\hat{\mathcal{H}}}^S$ is linear in the spin operators ${\hat{\mathbf{S}}}_j$ for each lattice site $j$, the RCS Hamiltonian ${\tilde{\mathcal{H}}}_{\mathrm{cl}}$ coincides with the usual classical model ${\mathcal{H}}_{\mathrm{cl}}={\lim }_{\mathcal{S}\to \infty }{\hat{\mathcal{H}}}^{\mathcal{S}}$. In the presence of non-linear terms, however, the RCS theory is more accurate than ${\mathcal{H}}_{\mathrm{cl}}$. For the many materials modeled by spin Hamiltonians with (non-linear) single-ion anisotropy terms, the use of the RCS theory is essential to accurately model phase diagrams and to extract the correct Hamiltonian parameters from neutron scattering data

5 pages, 1 figures

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