Emergent Quantum Phase Transition of a Charge-Density-Wave Insulator

There are two broad classes of phase transitions known in critical phenomena: thermal phase transitions, which typically go from an ordered phase to a disordered phase (driven by thermal fluctuations) and quantum phase transitions, which typically go from an ordered phase to a quantum coherent phase at zero temperature (driven by quantum fluctuations). Here, we introduce a new class of transitions that lie in between these two, which we call an emergent quantum phase transition. This system has no quantum phase transition at T=0, but it has a transition (here a metal-to-insulator transition) that is present for all nonzero T including the limit as T approaches 0. At nonzero temperatures, the system displays similar behavior to that of a quantum-critical system, with scaling behavior seen in the resistivity, but the emergent quantum critical point does not arise from a thermal critical point being suppressed to T=0. We illustrate this phenomena with an exact solution of the emergent metal-insulator transition of the charge-density-wave phase in an electronic system that also has both thermal order-disorder transitions and a Mott-like metal-insulator transition. We discuss the origin of this phase through thermally activated defect states, and how one can identify this behavior in experimental systems. We also describe how it may also appear in spin-density-wave antiferomagnets in three dimensions.