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 and the scaling form ,T = 1 2 F 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 , 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.