Phase diagram of interacting spinless fermions on the honeycomb lattice

摘要: Fermions hopping on a hexagonal lattice represent one of the most active research fields in condensed matter since discovery graphene 2004 and its numerous applications. Another exciting aspect interplay between geometry quantum mechanical effects is given by Haldane model (Haldane 1988 Phys. Rev. Lett. 61 2015), where spinless fermions experiencing certain flux pattern honeycomb leads to stabilization topological phase matter, distinct from Mott insulator nowadays dubbed Chern insulator. In this context, it crucial understand role interactions review will describe recent results that have been obtained for minimal model, namely with nearest next-nearest neighbour density-density at half-filling. Topics addressed include an introduction discussion possible instabilities Dirac semimetal, presentation various theoretical numerical approaches, summary particular emphasis stability or not some exotic phases such as charge ordered ones (similar Wigner crystals) spontaneous phases.