Phase diagram of hard-core bosons on clean and disordered 2-leg ladders: Mott insulator - Luttinger liquid - Bose glass

One dimensional free-fermions and hard-core bosons are often considered to be equivalent. Indeed, when restricted to nearest-neighbor hopping on a chain the particles cannot exchange themselves, and therefore hardly experience their own statistics. Apart from the off-diagonal correlations which depends on the so-called Jordan-Wigner string, real-space observables are similar for free-fermions and hard-core bosons on a chain. Interestingly, by coupling only two chains, thus forming a two-leg ladder, particle exchange becomes allowed, and leads to a totally different physics between free-fermions and hard-core bosons. Using a combination of analytical (strong coupling, field theory, renormalization group) and numerical (quantum Monte Carlo, density-matrix renormalization group) approaches, we study the apparently simple but non-trivial model of hard-core bosons hopping in a two-leg ladder geometry. At half-filling, while a band insulator appears for fermions at large interchain hopping tperp >2t only, a Mott gap opens up for bosons as soon as tperp\neq0 through a Kosterlitz-Thouless transition. Away from half-filling, the situation is even more interesting since a gapless Luttinger liquid mode emerges in the symmetric sector with a non-trivial filling-dependent Luttinger parameter 1/2\leq Ks \leq 1. Consequences for experiments in cold atoms, spin ladders in a magnetic field, as well as disorder effects are discussed. In particular, a quantum phase transition is expected at finite disorder strength between a 1D superfluid and an insulating Bose glass phase.