Holstein model and Peierls instability in one-dimensional boson-fermion lattice gases

We study an ultracold Bose-Fermi atomic mixture in a one-dimensional optical lattice. When boson atoms are heavier then fermion atoms the system is described by an adiabatic Holstein model, exhibiting a Peierls instability for commensurate fermion filling factors. A bosonic density wave with a wave number of twice the Fermi wave number will appear in the quasi-one-dimensional system, due to the opening of a gap at the Fermi energy in the fermion spectrum.