Quantum Criticality and Possible Superconductivity in Z_n Anisotropic Quantum Rotor Model Coupled with Free Fermion

Quantum rotor model with Zn clock term (Zn anisotropic quantum rotor model) is known to exhibit a U(1) symmetric quantum critical point between Z_n symmetry breaking phase and quantum disorder phase for n ≥ 4. Around such quantum critical point, gapped bosonic excitations in the two phases become massless. Thereby, a coupling between a local boson degree of freedom and a free fermion could lead a superconductivity near the critical point. Motivated by this anticipation, we mapped the model into an electric flux model with electric charge, and carried out a quantum Monte-Carlo simulation study with a global update. Based on a finite-size scaling analysis of a superfluid stiffness parameter and comparison with the critical exponent of the 3D XY universality class, we discuss the critical nature of the quantum critical point . If the time allows, we discuss the possible superconducting pairing instability in the fermion system.