Quantum critical paraelectrics and the Casimir effect in time

We study the quantum paraelectric-ferroelectric transition near a quantum critical point, emphasizing the role of temperature as a “finite-size effect” in time. The influence of temperature near quantum criticality may thus be likened to a temporal Casimir effect. The resulting finite-size scaling approach yields 1/T² behavior of the paraelectric susceptibility (χ) and the scaling form χ(ω,T)=1/ω²F(ω/T), recovering results previously found by more technical methods. We use a Gaussian theory to illustrate how these temperature dependences emerge from a microscopic approach; we characterize the classical-quantum crossover in χ, and the resulting phase diagram is presented. We also show that coupling to an acoustic phonon at low temperatures (T) is relevant and influences the transition line, possibly resulting in a reentrant quantum ferroelectric phase. Observable consequences of our approach for measurements on specific paraelectric materials at low temperatures are discussed.