Paradigm shift for quantum paraelectric: softening of longitudinal modes

We revisit the quantum phase transition from a paraelectric state to a ferroelectric one and in particular the widespread distinction between a longitudinal modes to transverse one. In contrast to transitions at finite temperature, for a quantum phase transition breaking a discrete symmetry the splitting between the modes is irrelevant. We show that an anisotropy in the context of a quantum phase transition leads to a different behavior, compared to a classical transition, and suggest an experiment to observe it. The result is essential for explaining the pairing mechanism in strontium titanate.