Philipp Hauke^1,*, Fernando M. Cucchietti,¹ Alexander Müller-Hermes,² Mari-Carmen Bañuls,² J. Ignacio Cirac,² and Maciej Lewenstein^1,3a
1 ICFO - Institut de Cie`ncies Foto`niques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain
2 Max-Planck-Institut fu"r Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
3 ICREA - Institucio` Catalana de Ricerca i Estudis Avanc,ats, E-08010 Barcelona, Spain
(Dated: October 9, 2010)

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many meta-stable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization, and quasiexact numerical techniques (density-matrix renormalization group and infinite time evolving block decimation). We find that the complete devil's staircase -- an infinite sequence of crystal states existing at vanishing tunneling -- spreads to a succession of lobes similar to the Mott-lobes found in Bose-Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar two-dimensional models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long range (algebraic) correlations, opposed to models with nearest-neighbor tunneling which show exponential decay of correlations.

* Electronic address: Philipp.Hauke@icfo.es