The quantum Kibble-Zurek mechanism: the role of boundary conditions, endpoints and kink types

Quantum phase transitions are characterised by the universal scaling laws in the critical region surrounding the transitions. This universality is also manifested in the critical real-time dynamics through the quantum Kibble-Zurek mechanism. In recent experiments on a Rydberg atom quantum simulator, the Kibble-Zurek mechanism has been used to probe the nature of quantum phase transitions. In this paper we analyze the caveats associated with this method and develop strategies to improve its accuracy. Focusing on two minimal models -- transverse-field Ising and quantum three-state Potts, both in one dimension -- we study the effect of boundary conditions, the location of the endpoints and some subtleties in the definition of the kink operators. In particular, we show that the critical scaling of the most intuitive types of kinks is extremely sensitive to the correct choice of endpoint, while more advanced types of kinks exhibit remarkably robust universal scaling. Furthermore, we show that when kinks are tracked over the entire chain, fixed boundary conditions improve the accuracy of the scaling. Surprisingly, the Kibble-Zurek critical scaling appears to be equally accurate whether the fixed boundary conditions are chosen to be symmetric or anti-symmetric. We also show that the density of kinks extracted in the central part of long chains obeys the predicted universal scaling for all types of boundary conditions. Finally, we test our kink definition for the Ising transition on the period-2 phase of the Rydberg model and show that it is more robust against the end point than the standard definition.