  We examine a bosonic two-leg ladder model subject to a magnetic flux, and
especially focus on a regime where the lower energy band has two minima. By
using a low-energy field theory approach, we study several issues discussed in
the system: the existence of local patterns in density and current,
chiral-current reversal, and the effect of a nearest-neighbor interaction along
the rung direction. In our formalism, the local patterns are interpreted as a
result of breaking of discrete symmetry. The chiral-current reversal occurs
through a competition between a current component determined at a commensurate
vortex density causing an enlargement of the unit cell, and another component,
which is proportional to the magnetic field doping from the corresponding
commensurate flux. The nearest-neighbor interaction along the rung direction
available with the technique on a synthetic dimension is shown to favor a
population-imbalance solution in an experimentally relevant regime.
