Unconventional U(1) to ${\mathbf{Z}}_{\mathbf{q}}$ cross-over in quantum and classical $\mathbf{q}$-state clock models

Pranay Patil, Hui Shao, Anders W. Sandvik

We consider two-dimensional $q$-state quantum clock models with quantum fluctuations connecting states with clock transitions with different choices for matrix elements. We study t…