Rydberg-excited atoms have provided an experimental realization of strong repulsive non-local van der Waals interactions [1]. In two and three dimensions, it was showed theoretically that these soft-core interactions can engender exotic phases such as supersolid states.

In the present work, we study the quantum phases of one-dimensional soft-core systems. They can be described by a longer-range extended Hubbard model with frustrating couplings.
The phase diagram of spinless fermions interacting via these finite-range soft-core potentials, exhibits a quantum liquid phase beyond the Tomonaga-Luttinger liquid picture [2]. It involves new features such as cluster-type correlation functions.
We continue the study of this phase diagram and we also introduce a spin degree of freedom.

References:

[1] N. Henkel, R. Nath, and T. Pohl, PRL 104 195302 (2010) (and more)

[2] M. Mattioli, M. Dalmonte, W. Lechner and G. Pupillo
Cluster Luttinger liquids of Rydberg-dressed gases in optical lattices
arXiv:1304.3012