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We consider a Bose-Hubbard ladder subject to an artificial magnetic flux anddiscuss its different ground states, their physical properties, and the quantumphase transitions between them. A low-energy effective field theory is derived,in the two distinct regimes of a small and large magnetic flux, using abosonization technique starting from the weak-coupling limit. Based on thiseffective field theory, the ground-state phase diagram at a filling of oneparticle per site is investigated for a small flux and for a flux equal to$\pi$ per plaquette. For $\pi$-flux, this analysis reveals a tricritical pointwhich has been overlooked in previous studies. In addition, the Mott insulatingstate at a small magnetic flux is found to display Meissner currents.

Ground States of a Bose-Hubbard Ladder in an Artificial Magnetic Field: Field-Theoretical Approach