Quantum field theory for the chiral clock transition in one spatial dimension

Understand

We describe the quantum phase transition in the $N$-state chiral clock model in spatial dimension $d=1$.

• With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms.
• For such couplings and $N=3$, the clock model is expected to have a direct phase transition from a gapped phase with a broken global $\mathbb{Z}_N$ symmetry, to a gapped phase with the $\mathbb{Z}_N$ symmetry restored.
• The transition has dynamical critical exponent $z \neq 1$, and so cannot be described by a relativistic quantum field theory.