Frustrated Bose ladder with extended range density-density interaction

When hard-core bosons on a two-leg ladder get frustrated by ring exchange interactions, the elusive $d$-wave Bose liquid (DBL) can be stabilized, a bosonic analog of a correlated metal. Here, we analyze the effect of extended Hubbard interactions on the DBL phase. Strikingly, these interactions are found to act in favor of the exotic Bose liquid. This observation is of immediate relevance for physical systems in which nonlocal exchange processes occur as a consequence of extended range density-density interactions. Our observation also helps to achieve DBL physics in a synthetic-dimension ladder, where on-site interactions translate into nonlocal interactions along a synthetic rung. In this context, we also consider the extreme limit, in which the local hard-core constraint is elevated to an effective rung blockade. In addition to the enhancement of DBL physics due to extended range density-density interactions, we also find signatures of an interesting intermediate phase between the superfluid and the DBL regime. This phase, called the density-modulated $s$-wave pairing phase, combines features of density wave and $s$-wave pairing. Our results offer insights into the physics of frustrated bosons by highlighting the influence of density-density interaction and rung blockade.