Persisting Meissner state and incommensurate phases of hard-core boson ladders in a flux

The phase diagram of a half-filled hard core boson two-leg ladder in a flux is investigated by means of numerical simulations based on the Density Matrix Renormalization Group (DMRG) algorithm and bosonization. We calculate experimentally accessible observables such as the momentum distribution, as well as rung current, density wave and bond-order wave correlation functions, allowing us to identify the Mott Meissner and Mott Vortex states. We follow the transition from commensurate Meissner to incommensurate Vortex state at increasing interchain hopping till the critical value [Piraud et al. Phys. Rev. B v. 91, p. 140406 (2015)] above which the Meissner state is stable at any flux. For flux close to $\pi$, and below the critical hopping, we observe the formation of a second incommensuration in the Mott Vortex state that could be detectable in current experiments.