Renormalized Classical Theory of Quantum Magnets

The classical limit of a spin system traditionally involves replacing spins on each site with classical dipoles. This is done by restricting the states to products of SU(2) coherent states and substituting operators with their expectation values in the S→∞ limit. However, when S is greater than ½, spins encompass not only dipolar degrees of freedom, but also higher-order multipole moments. In such cases, it is often advantageous to adopt an alternative limit, relying on coherent states of SU(2S+1), which can represent these additional degrees of freedom clasically. Although many systems with S>½ exhibit predominantly dipolar dynamics, our study demonstrates that, even in such scenarios, employing the alternative limit and constraining the resulting dynamics to a dipolar phase space (CP¹) yields a more precise theory than that derived in the large-S limit. Importantly, the new theory can be obtained through a straightforward renormalization of the traditional one. We explore the implications of this approach for estimating model parameters from scattering data, constructing phase diagrams, and advancing our comprehension of multi-flavor spin wave theories. More broadly, this work proposes a universal method for developing computationally efficient classical models that encompass quantum effects.