  The simplest quantum generalization of the six-vertex model describes
fluctuations of the order parameter of the d-density wave (DDW), believed to
compete with superconductivity in the high-Tc superconductors. The ground state
of this model undergoes a first order transition from the DDW phase to a
resonating plaquette phase as the quantum fluctuations are increased, which is
explored with the help of quantum Monte Carlo simulations and analytic
considerations involving the n-vector (n=2) model with cubic anisotropy. In
addition to finding a new quantum state, we show that the DDW is robust against
a class of quantum fluctuations of its order parameter. The inferred finite
temperature phase diagram contains unsuspected multicritical points.

Superconductivity;Strongly Correlated Electrons