  We introduce variational wave functions to evaluate the ground-state
properties of spin-phonon coupled systems described by the Su-Schrieffer-Heeger
model. Quantum spins and phonons are treated on equal footing within a Monte
Carlo sampling, and different regimes are investigated. We show that the
proposed variational Ansatz yields good agreement with previous density-matrix
renormalization group results in one dimension and is able to accurately
describe the spin-Peierls transition. This variational approach is neither
constrained by the magnetoelastic-coupling strength nor by the dimensionality
of the systems considered, thus allowing future investigations in more general
cases, which are relevant to spin-liquid and topological phases in two spatial
dimensions.
