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

TL;DR

This study investigates the phase glass and quantum phase transition in a two-dimensional disordered quantum rotor model, revealing a glassy phase with long-range order and critical behavior near a Mott insulator transition.

Contribution

It provides the first detailed analysis of the phase glass phase and quantum critical properties in a 2D disordered quantum rotor model using Monte Carlo simulations.

Findings

Identification of a phase glass with finite compressibility and long-range order.

Determination of critical exponents: $z_{dyn} \,\simeq\, 1.17$, $\nu \simeq 0.73$, $\nu_z \simeq 0.85$.

Speculation that the phase glass is superconducting at zero current.

Abstract

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-ranged phase rigidity in both spatial and imaginary time directions. 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 $z_{\rm dyn}\simeq 1.17$ is greater than one. Correlation length exponents in the spatial and imaginary time directions are given by $\nu\simeq 0.73$ and $\nu_z\simeq 0.85$, 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.