Renormalized Classical Theory of Quantum Magnets

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 \(\hat{\cal{H}}^{S}\) is linear in the spin operators \(\hat{\boldsymbol{S}}_j\) for each lattice site \(j\), the RCS Hamiltonian \(\tilde{\cal{H}}_{\rm cl}\) coincides with the usual classical model \(\cal{H}_{\rm cl} = \lim_{S\rightarrow\infty} \hat{\cal{H}}^S\). In the presence of non-linear terms, however, the RCS theory is more accurate than \(\cal{H}_{\rm cl}\). 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