Classical techniques for the characterization of magnetic excitations at finite temperatures

In a classical limit, a very high dimensional, linear quantum dynamics is replaced by a much lower dimensional, nonlinear dynamics. Despite the radical reduction in dimensionality and computational complexity, classical techniques have proven effective at describing a wide range of quantum magnets, including some that fail to order entirely. This suggests that many magnetic systems lie close to some classical limit, and that the geometric and nonlinear aspects introduced in a classical limit play an important role in their efficacy. Moreover, by modulating temperature and external field, even systems that display fundamentally quantum behavior can be forced into a classical regime where an appropriate classical limit can be used to extract Hamiltonian parameters. It is important to note, however, that the choice of a classical limit is not unique, and it is generally necessary to apply various corrections and renormalizations in order to achieve good correspondence with exact or experimental results. This talk will review a family of classical limits that can be derived by starting from a product of SU(N) coherent states, the formalism that has been implemented in the Sunny software package. Geometric aspects of these states will be discussed, and it will be shown how their classical dynamics can be formulated as a nonlinear Schrödinger equation. The resulting geometric picture leads to a number of interaction renormalizations that are otherwise difficult to derive and understand. Several case studies will demonstrate the application of alternative classical limits, paying particular attention to the low-temperature correspondence with generalized spin wave theories and the crossover to classical behavior that occurs at high temperatures. Prospects for more rigorous treatment of both quantum and thermal fluctuations in intermediate temperature regimes, where the nonlinear effects of the classical dynamics are most pronounced, will also be discussed.