Quantum criticalities with lattice vibrations*

Quantum criticality is one of the most important concepts in modern condensed matter physics, as novel physics may arise in the vicinity of the quantum critical point by quantum fluctuations. These fluctuations inevitably couple to lattice vibrations in real materials due to the lattice structures. It is well understood that a class of thermal continuous transitions on lattices is eventually destabilized by either macroscopic instability of lattice structures or induced first-order symmetry breaking transitions. However, for the quantum phase transition, little is known about its consequences. Here, we demonstrate that such interplay between quantum criticality and lattice vibration leads to a new class of quantum many-particle phenomena. Moreover, we suggest a new stability condition for these criticalities which generalizes the specific-heat criterion of thermal transitions to a quantum version. Our results suggest a new direction to find novel quantum criticalities in nature.