We study the phase diagram of strongly interacting fermions in one dimension at finite temperature, with mass and spin imbalance. By including the possibility of the existence of a spatially inhomogeneous ground state, we find regions where spatially varying superfluid phases are favored over homogeneous phases. We obtain estimates for critical values of the temperature, mass, and spin imbalance, above which these phases disappear. Finally, we show that an intriguing relation exists between the general structure of the phase diagram and the binding energies of the underlying two-body bound-state problem. Although our present study of the many-body aspects is based on a mean-field approximation, it may still yield phenomenologically important insights into the dynamics of strongly interacting fermions in one dimension. Most importantly, however, we expect that our present mean-field study can be considered worthwhile from a field-theoretical point of view as it may help to better understand the mechanisms underlying the emergence of inhomogeneous phases in higher dimensions as well as the general structure of the associated phase diagrams.

• Received 8 November 2013

DOI:https://doi.org/10.1103/PhysRevA.89.063609