Recent experiments on one-dimensional Rydberg simulators display quantum phase transitions to spatially ordered crystals with a period of N sites [1]. These experiments are capable of probing the universal Kibble-Zurek dynamics of the transitions, allowing experimental access to critical exponents [2]. For N>2, these transitions are in the same universality class as the Z_N chiral clock model, which exhibits a rich phase structure. In particular, this model displays a direct continuous phase transition between a gapped symmetric phase and a gapped phase with broken Z_N symmetry for certain values of N. I will present the universal quantum field theory for this transition, where the main theoretical tool is a non-local duality mapping to a theory describing the condensation of domain walls. A renormalization group analysis of the field theory gives the first analytic predictions for the critical exponents, which are compared to experimental and numerical results [3].

[1] Bernien et. al., Nature, 551, 579 (2017).

[2] Keesling et. al., arXiv:1809.05540.

[3] SW, R. Samajdar, S. Sachdev, Phys. Rev. B., 98, 205118 (2018).