  Most nonperturbative numerical studies of electron-phonon interactions focus
on model Hamiltonians where the electrons interact with a phonon branch via a
single type of microscopic mechanism. Two commonly explored couplings in this
context are the Holstein and Su-Schrieffer-Heeger (SSH) interactions, which
describe phonons modulating the on-site energy and intersite electron hopping,
respectively. Many materials, however, have multiple phonon branches that can
each interact with electronic degrees of freedom in different ways. We present
here a determinant quantum Monte Carlo study of the half-filled two-dimensional
(bond) SSH-Holstein Hamiltonian, where electrons couple to different phonon
branches via either the Holstein or SSH mechanism. We map the model's phase
diagram and determine the nature of the transitions between charge-density
wave, bond order wave, and antiferromagnetic order.
