Motivated by the discovery of the coexistence of unfrozen spin and dipole fluctuations
in an organic quantum spin liquid called κ-H₃(Cat-EDT-TTF)₂ [1], we propose a new
asymptotically solvable model, where a quantum spin liquid (resonating valence bond) state is
accompanied by quantum proton motion, which we name quantum valence bond ice. We can
regard this state as a quantum spin-dipole liquid in the sense that quantum spin fluctuations
are triggered by the coupling to the quantum proton motion. In the classical version
of this model, there are macroscopically degenerate ground states, and quantum fluctuations
of the proton motion will lift the degeneracy. The resulting quantum ground state should be
regarded as the U(1) spin liquid phase in 3 dimensions, connected to Anderson's resonating
valence bond state [2] in the perturbative level.
[1] M. Shimozawa et al., Nat. Commun., 8, 1821 (2017).
[2] P. W. Anderson, Mater. Res. Bull., 8, 153 (1973).