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 effe
cts 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.
We present a pedagogical review of the physics of fractional Chern insulators with a particular focus on the connection to the fractional quantum Hall effect. While the latter conventionally arises in semiconductor heterostructures at low temperature
s and in high magnetic fields, interacting Chern insulators at fractional band filling may host phases with the same topological properties, but stabilized at the lattice scale, potentially leading to high-temperature topological order. We discuss the construction of topological flat band models, provide a survey of numerical results, and establish the connection between the Chern band and the continuum Landau problem. We then briefly summarize various aspects of Chern band physics that have no natural continuum analogs, before turning to a discussion of possible experimental realizations. We close with a survey of future directions and open problems, as well as a discussion of extensions of these ideas to higher dimensions and to other topological phases.
Unstable 10C nuclei are produced as quasi-projectiles in 12C+24Mg collisions at E/A = 53 and 95 MeV. The decay of their short-lived states is studied with the INDRA multidetector array via multi-particle correlation functions. The obtained results sh
ow that heavy-ion collisions can be used as a tool to access spectroscopic information of unbound states in exotic nuclei, such as their energies and the relative importance of different sequential decay widths.
Unbound states of $^{10}$C nuclei produced as quasi-projectiles in $^{12}$C+$^{24}$Mg collisions at E/A = 53 and 95 MeV are studied with the Indra detector array. Multi-particle correlation function analyses provide experimental evidence of sequentia
l de-excitation mechanisms through the production of intermediate $^{9}$B, $^{6}$Be and $^{8}$Be unbound nuclei. The relative contributions of different decay sequences to the total decay width of the explored states is estimated semi-quantitatively. The obtained results show that heavy-ion collisions can be used as a tool to access spectroscopic information about exotic nuclei.
