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Gauge Field and Confinement-Deconfinement Transition in Hydrogen-Bonded Ferroelectrics

Quantum melting of ferroelectric moment in the frustrated hydrogen-bonded system with "ice rule" is studied theoretically by using the quantum Monte Carlo simulation. The large number of nearly degenerate configurations are described as the gauge degrees of freedom, i.e., the model is mapped to a lattice gauge theory which shows the confinement-deconfinment transition (CDT). The dipole-dipole interaction $J_2$, on the other hand, explicitly breaks the gauge symmetry leading to the ferroelectric transition (FT) at finite temperature $T$. It is found that the crossover from FT to CDT manifests itself in the reduced correlation length of the polarization $ξ_{\text{FT}} \sim Δ(K-K_c)^{-ν}$ with $Δ\propto \sqrt{J_2}$ while $K_c$ and $ν$ remains finite in the limit $J_2 \to 0$. In contrast, the Currie-Weiss-like law for the susceptibility $χ$ and the spontaneous polarization behaves smoothly and the length scale $ξ_{\text{CDT}}$, related to the molecular symmetry and volume for CDT, does not reduce in this limit.