The state of a system and its characteristic excitations change qualitatively when undergoing a phase transition. At a second order phase transition, these excitations are subject to strong fluctuations and if the transition happens at zero temperature, the quantum as opposed to the thermal origin of fluctuations can be revealed.
In particular, order-parameter and electronic fluctuations are strongly coupled near a quantum phase transition in a metal and must be treated on equal footing. As a result, the critical behavior in the vicinity of the quantum transition differs from its classical counterpart. The characterization of the corresponding new universality classes is an issue of fundamental interest.
Furthermore, the coupling between order-parameter and electronic fluctuations gives rise to a complex interplay of incoherence and non-Fermi-liquid behavior on the one side, and mediation of attraction and pairing tendencies on the other side, which is believed to be responsible for the rich phase diagram of several strongly correlated electron systems.
We study these different aspects of quantum phase transitions motivated by Dirac materials, high-temperature superconductors or heavy-fermion materials. We investigate how the critical behavior manifests itself in thermodynamic or transport observables and who wins the competition between non-Fermi liquid and pairing.