Ground States of a Bose-Hubbard Ladder in an Artificial Magnetic Field:   Field-Theoretical Approach
  We consider a Bose-Hubbard ladder subject to an artificial magnetic flux and discuss its different ground states, their physical properties, and the quantum phase transitions between them. A low-energy effective field theory is derived, in the two distinct regimes of a small and large magnetic flux, using a bosonization technique starting from the weak-coupling limit. Based on this effective field theory, the ground-state phase diagram at a filling of one particle 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 point which has been overlooked in previous studies. In addition, the Mott insulating state at a small magnetic flux is found to display Meissner currents. 
Akiyuki Tokuno and Antoine Georges
cond-mat.quant-gas cond-mat.str-el