Emergent Symmetry U(1) and Tricriticality in a 2D Quantum Clock Model*

We propose a quantum clock model on the square lattice built out of
a q-state classical clock model with a quantum fluctuation (a
generalization of a transverse field) added to it. We see evidence that
this model is closely related to the 3D classical clock model through the
standard quantum to classical mapping. For q>=5, we see a continuous
phase transition and for q=5,6 we show that, at the phase transition, an
emergent U(1) symmetry appears, similar to the 3D classical clock models.
We address the connection that this emergent symmetry has to a
second length scale within the scenario of dangerously irrelevant
perturbations of the XY model. We also demonstrate the existence of
a tricritical point in the case of q=4, which can be tuned by
changing the form of the quantum fluctuation operator.