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Quantum Monte Carlo study of the formation of molecular polarizations and the antiferroelectric ordering in squaric acid crystals

Effects of geometrical frustration and quantum fluctuation are theoretically investigated for the proton ordering in a quasi-two-dimensional hydrogen-bonded system, squaric acid crystal. We elucidate the phase diagram for an effective model, the transverse-field Ising model on a frustrated checkerboard lattice, by using quantum Monte Carlo simulation. A crossover to liquidlike paraelectric state with well-developed molecular polarizations is identified, distinguishably from long-range ordering. Emergence of long-range order from the liquidlike state exhibits peculiar aspects originating from the lifting of quasi-macroscopic degeneracy, such as colossal enhancement of the transition temperature and a vanishingly small anomaly in the specific heat.