Quantum criticalities induced by Lifshitz transitions

We study electron correlation effects on quantum criticalities of Lifshitz transitions (LTs), using the mean-field theory based on a preexisting broken symmetry order, in two-dimensional systems. In the presence of interactions, LTs may become discontinuous in contrast to the continuous transition in the original proposal by Lifshitz for noninteracting systems. We find that the quantum criticality at the endpoint of discontinuous LTs, which we call the marginal quantum critical point, belongs to a different universality class from that of the mean-field Ising model.