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We present the first approximation free diagrammatic Monte Carlo study of alattice polaron interacting with an acoustic phonon branch through thedeformation potential. Weak and strong coupling regimes are separated by aself-trapping region where quantum resonance between various possible latticedeformations is seen in the ground state properties, spectral function, andoptical conductivity. The unique feature of such polaron is the interplaybetween long- and short wavelength acoustic vibrations creating a compositephonon cloud and leading to persistent self-trapping due to the existence ofmultiple quasi-stable states. This results in a spectral response whosestructure is much more complex than in any of the previously considered polaronmodels.

Diagrammatic quantum Monte Carlo study of an acoustic lattice polaron