  Polaron and bipolaron formation in the Holstein-Hubbard model with harmonic
confinement potential, relevant to quantum dot structures, is investigated in
one to three dimensions by means of unbiased quantum Monte Carlo simulations.
The discrete nature of the lattice and quantum phonon effects are fully taken
into account. The dependence on phonon frequency, Coulomb repulsion,
confinement strength (dot size) and electron-phonon interaction strength is
studied over a wide range of parameter values. Confinement is found to reduce
the size of (bi-)polarons at a given coupling strength, to reduce the critical
coupling for small-(bi-)polaron formation, to increase the polaron binding
energy, and to be more important in lower dimensions. The present method also
permits to consider models with dispersive phonons, anharmonic confinement, or
long-range interactions.
