Variational wave functions for spin-phonon models

The existence and stability of spin-liquid phases represents one of the central topics in the field of frustrated magnetism. In the last few years, a large theoretical effort has been devoted to proposing and studying frustrated spin models which could host spin-liquid ground states. Although several examples of well-established spin-liquid phases are now available, the question of the stability of these states to the coupling between spins and lattice distortions (i.e. phonons) has been scarcely investigated. As suggested by the well-known one-dimensional case, the effect of phonons can cause a Peierls instability of spin-liquid phases towards the formation of valence-bond order.

In this talk we present a variational framework for the study of spin-phonon models in which lattice distortions affect the exchange interaction between the spins. Our method, based on Jastrow-Slater wave functions and Monte Carlo sampling, provides a full quantum treatment of both spin and phonon degrees of freedom. We first assess the accuracy of our variational scheme by comparing our results for the spin-Peierls chain with other numerical methods [Phys. Rev. B 102, 125149 (2020)]. Then, we discuss the effects of the spin-phonon coupling on the spin-liquid phases of two-dimensional frustrated models.