Variational wave functions for spin models with phonons and anisotropic-exchange couplings

The definition of variational wave functions represents an invaluable tool to describe strongly-correlated systems. Examples are given by the Bardeen-Cooper-Schrieffer theory of superconductivity and the Laughlin's explanation of the fractional quantum Hall effect. A promising playground where this kind of approach has been fruitfully applied lies in highly-frustrated spin models, where the spin-liquid phases may emerge from the competition of various super-exchange interactions. These exotic states of matter are characterized by high entanglement, fractional excitations, and topological properties. Gutzwiller-projected wave functions (constructed from fermionic and bosonic constituents) have been employed since the pioneering suggestion by Anderson of the resonating-valence-bond theory. In the recent years, we demonstrated that the fermionic approach gives very accurate results in a wide range of SU(2) Heisenberg models on a wide variety of lattices (most importantly for the kagome lattice). The next challenge is now to incorporate further ingredients in the microscopic Hamiltonians, to get closer to actual materials. Examples are given by the inclusion of quantum phonons, the Dzyaloshinskii–Moriya interaction, and, more generally, anisotropic-exchange couplings (as present in Kitaev materials). Besides being relevant for an accurate description of real materials, these additional perturbations are extremely useful to assess the stability of spin-liquid phases, especially the gapless ones. In this talk, we discuss the accuracy of Gutzwiller-projected wave functions to determine the correct results of these extended models, focusing on the kagome lattice, which still continues to attract the attention of the community working on frustrated magnetism.