Monte Carlo Simulations of the Disordered q-state Quantum Clock model

In this work, we consider the one-dimensional q-state quantum clock model with bond disorder. We map the quantum Hamiltonian to a two-dimensional classical q-state clock model with nearest neighbor interactions and quenched columnar random bond disorder. We study the classical model using large-scale Monte Carlo simulations. The clean q-state clock model is known to exhibit an intermediate quasi long-range ordered phase between paramagnetic and true long-range ordered phases for q ≥ 5. To identify critical temperature of the phase transitions as the disorder strength is varied, we consider the spin-wave stiffness. Spin-wave stiffness is a measure of free energy response to a twist in boundary conditions. It is a dimensionless observable for a 2D system. We identify the phase boundaries between the paramagnetic, quasi-long-range ordered and clock-ordered phases, and evaluate critical exponents as the disorder is varied. The model shows a non-trivial crossover from a weak to a strong disorder regime.