Phase glass and zero-temperature phase transition in a randomly frustrated two-dimensional quantum rotor model

The ground state of the quantum rotor model in two dimensions with random phase frustration is investigated. Extensive Monte Carlo simulations are performed on the corresponding (2 + 1)-dimensional classical model under the entropic sampling scheme. For weak quantum fluctuation, the system is found to be in a phase glass phase characterized by a finite compressibility and a finite value for the Edwards-Anderson order parameter, signifying long-range phase rigidity in both spatial and imaginary time directions. The scaling properties of the model near the transition to the gapped, Mott insulator state with vanishing compressibility are analyzed. At the quantum critical point, the dynamic exponent z(dyn) similar or equal to 1.17 is greater than one. Correlation length exponents in the spatial and imaginary time directions are given by v similar or equal to 0.73 and v(z) similar or equal to 0.85, respectively; both assume values greater than 0.6723 of the pure case. We speculate that the phase glass phase is superconducting rather than metallic in the zero-current limit.