We analyse an array of linearly extended monodomain dipoles forming square and kagomé lattices. We find that its phase diagram contains two (distinct) finite-entropy kagomé ice regimes-one disordered, one algebraic-as well as a low-temperature ordered phase. In the limit of the islands almost touching, we find a staircase of corresponding entropy plateaux, which is analytically captured by a theory based on magnetic charges. For the case of a modified square ice array, we show that the charges ('monopoles') are excitations experiencing two distinct Coulomb interactions: a magnetic 'three-dimensional' one as well as a logarithmic 'two dimensional' one of entropic origin.

We study a frustrated dipolar array recently manufactured lithographically by Wang in order to realize the square ice model in an artificial structure. We discuss models for thermodynamics and dynamics of this system. We show that an ice regime can be stabilized by small changes in the array geometry; a different magnetic state, kagome ice, can similarly be constructed. At low temperatures, the square ice regime is terminated by a thermodynamic ordering transition, which can be chosen to be ferro- or antiferromagnetic. We show that the arrays do not fully equilibrate experimentally, and identify a likely dynamical bottleneck.

We study the groundstates of cold atomic gases on rotating optical lattices, as described by the Bose-Hubbard model in a uniform effective magnetic field. Mapping the bosons to composite fermions leads to the prediction of quantum Hall fluids that have no counterpart in the continuum. We construct trial wavefunctions for these phases, and perform numerical tests of the predictions of the composite fermion model. Our results establish the existence of strongly correlated phases beyond those in the continuum limit, and provide evidence for a wider scope of the composite fermion approach beyond its application to the lowest Landau-level.Ultra-cold atomic gases have become a very active field of study of strongly correlated quantum systems. While dilute Bose gases are typically in a weakly interacting regime, they can be driven into regimes of strong correlations by various means. The application of an optical lattice potential leads to a suppression of the kinetic energy relative to the interaction energy, and has allowed the experimental exploration of the quantum phase transition between Mott insulator and superfluid [1]. Rapid rotation of the atomic gas also leads to a quenching of the kinetic energy, into degenerate Landau levels [2], and a regime of strong interactions [3]. At low filling factor ν (defined as the ratio of the number of particles to the number of vortices) this is predicted to lead to very interesting strongly correlated phases [4] which can be viewed as bosonic versions of fractional quantum Hall effect (FQHE) states [5]. In order to access the low filling factor regime in experiment, it may be favourable to exploit the strong interactions that are available in optical lattice systems [6,7] for which methods exist in which to simulate uniform rotation (or equivalently a uniform magnetic field) [8][9][10]. This raises the interesting question: what are the correlated phases of atomic gases that are subjected both to an optical lattice and to rapid rotation?In this Letter, we study the interplay between the FQHE of bosons and the strong correlation imposed by an optical lattice potential. At sufficiently low particle density, the effect of the lattice has been shown to have negligible impact on the nature of the continuum Laughlin state at ν = 1 2 [7,10]. We focus on the possibility that there exist strongly correlated phases which have no counterpart in the continuum, but that appear as a direct consequence of both the lattice potential and rotation. To do so, we adapt the composite fermion (CF) theory [11,12] which has been shown to accurately describe rotating atomic Bose gases in the continuum [13,14], and apply this theory to rotating bosons on a lattice. Within mean-field theory, the lattice leads to the intricate Hofstadter spectrum for the composite fermions [15]. We predict a series of incompressible phases of bosons on the optical lattice, characterized by special relations of the flux density n φ and particle density n, and we construct trial wavefunctions describing these phases. Fro...

The fractional quantum Hall (FQH) effect illustrates the range of novel phenomena which can arise in a topologically ordered state in the presence of strong interactions. The possibility of realizing FQH-like phases in models with strong lattice effects has attracted intense interest as a more experimentally accessible venue for FQH phenomena which calls for more theoretical attention. Here we investigate the physical relevance of previously derived geometric conditions which quantify deviations from the Landau level physics of the FQHE. We conduct extensive numerical many-body simulations on several lattice models, obtaining new theoretical results in the process, and find remarkable correlation between these conditions and the many-body gap. These results indicate which physical factors are most relevant for the stability of FQH-like phases, a paradigm we refer to as the geometric stability hypothesis, and provide easily implementable guidelines for obtaining robust FQH-like phases in numerical or real-world experiments.