Spinless Fermionic ladders in a magnetic field

We study a system of interacting spinless fermions hopping on a two-leg ladder subject to an external magnetic field perpendicular to the ladder. At $1/2$-filling, we find a series of quantum phase transitions as a function of the magnetic field: these are either $U(1)$ Gaussian phase transitions between two phases with distinct types of long-range order or Berezinskii-Kosterlitz-Thouless transitions between ordered and gapless phases. At $1/4$-filling, we also find long-range order: a bond density wave or a staggered flux phase, each supporting excitations with fractional charge.