Evolution of static and dynamical density correlations of one-dimensional soft-core bosons from the Tonks-Girardeau limit to a clustering fluid

Repulsive soft-core atomic systems may undergo clustering if their density is high enough that core overlap is unavoidable. In one-dimensional bosonic quantum systems, it has been shown that this instability triggers a transition from a Luttinger liquid to various cluster Luttinger liquids. Here, we focus on the Luttinger liquid regime and theoretically study the evolution of key observables related to density fluctuations, which manifest a striking dependence on density. We tune the interaction so that the low-density regime corresponds to a TonksGirardeau gas and show that as the density is increased the system departs more and more from Tonks-Girardeau behavior, displaying a much larger compressibility as well as rotonic excitations that finally drive the clustering transition. We compare various theoretical approaches, which are accurate in different regimes. Using quantum Monte Carlo methods and analytic continuation as a benchmark, we investigate the regime of validity of the mean-field Bogoliubov and the real-time multiconfiguration time-dependent Hartree-Fock approaches. Part of the behavior that we describe should be observable in ultracold Rydberg-dressed gases, provided that system losses are prevented.

Automated summary

In this study, we focus on the clustering behavior of repulsive soft-core atomic systems at high densities, and investigate the transition from a Luttinger liquid to various cluster Luttinger liquids. The evolution of key observables related to density fluctuations exhibits a strong dependence on density, with the system displaying larger compressibility and rotonic excitations as density increases, ultimately leading to the clustering transition. Different theoretical approaches are compared for accuracy in different regimes, with the behavior described potentially observable in ultracold Rydberg-dressed gases.