Why first order quantum phase transitions are interesting

It is frequently argued that only second order phase transitions at T = 0 deserve to be called quantum phase transitions, while first order quantum phase transitions are a contradiction in terms. However, quantum phase transitions differ from classical phase transitions in two fundamental ways. First, the free energy landscape need not be that of a classical second order phase transition for quantum fluctuations to drive the transition. Second, at T = 0 a rich variety of quantum correlation effects, such as magnetic rotons, instantons or skyrmion textures, are possible. The recent discovery of partial magnetic order, an extended non-Fermi liquid phase and superconductivity at the first order quantum phase transitions of itinerant-electron magnets underscore the need for detailed experimental studies of hitherto unexplored weak rigidities that are well known to generate first order behaviour. These include changes of the electronic valence, spin-orbit coupling, crystal electric field levels, and crystallographic structure driven by instabilities of the Fermi surface.