  Geometric frustrations and quantum mechanical fluctuations may prohibit the
formation of long-range ordering even at the lowest temperature, and therefore
liquid-like ground states could be expected. A good example is the quantum spin
liquid in frustrated magnets that represents an exotic phase of matter and is
attracting enormous interests. Geometric frustrations and quantum fluctuations
can happen beyond magnetic systems. Here we propose that quantum
electric-dipole liquids, analogs to quantum spin liquids, could emerge in
frustrated dielectrics where antiferroelectrically coupled small electric
dipoles reside on a triangular lattice. The quantum paraelectric hexaferrite
BaFe12O19, in which small electric dipoles originated from the off-center
displacement of Fe3+ in the FeO5 bipyramids constitute a two-dimensional
triangular lattice, represents a promising candidate to generate the
anticipated electric-dipole liquid. We present a series of experimental
evidences, including dielectric permittivity, heat capacity, and thermal
conductivity measured down to 66 mK, to reveal the existence of a nontrivial
ground state in BaFe12O19, characterized by itinerant low-energy excitations
with a small gap, to which we interpret as an exotic liquid-like quantum phase.
The quantum electric-dipole liquids in frustrated dielectrics open up a fresh
playground for fundamental physics and may find applications in quantum
information and computation as well.
