  In most cases, as the strength of electron-phonon coupling increases, the
effective mass of polarons typically increases. However, in this paper, we
uncover a fascinating phenomenon: the presence of light polarons even within
the strong coupling regime, where electron-phonon coupling includes both
Holstein and bond types (electron-phonon coupling occurring on the hopping
bonds). To investigate this, we employ a novel Diagrammatic Monte Carlo method
based on the path-integral formulation of the particle sector and the
Fock-state representation of the phonon sector. Our study centers on analyzing
the impact of bond electron-phonon coupling on the Holstein polaron's essential
properties, including its effective mass, ground state energy, and the average
number of phonons. We examine two distinct scenarios: one where the phonon
frequency of both Holstein and bond types is the same, and another where the
phonon frequency of the Holstein type is twice as large as that of the bond
type. In both of these two cases, when the Holstein coupling falls within the
light mass regime, we observe minimal changes in the effective mass as a
function of bond coupling, compared to the case of the bare bond polaron.
However, the behavior of the effective mass undergoes a significant change in
the heavy mass regime. Most intriguingly, we discover a non-monotonic
dependence of the effective mass on the bond coupling $g_B$ when the Holstein
coupling $g_H$ falls within the heavy mass regime. This finding holds promise,
particularly in the context of bipolaron, where achieving a light effective
mass and a large binding energy to get the compact size, is crucial.
