Conformal and chiral phase transitions in Rydberg chains

TL;DR

This paper uses advanced simulations to analyze phase transitions in Rydberg chains, identifying conformal points and proposing benchmarks for experimental verification of chiral universality classes.

Contribution

It maps wave-vectors in Rydberg chains, characterizes conformal transitions, and suggests experimental benchmarks for chiral phase transitions.

Findings

Confirmed 3-state Potts universality for period-3 phase transition.

Identified Ashkin-Teller universality with ν≈0.80 for period-4 phase transition.

Proposed conformal points as benchmarks for Kibble-Zurek experiments.

Abstract

Using density matrix renormalization group simulations on open chains, we map out the wave-vector in the incommensurate disordered phase of a realistic model of Rydberg chains with $1/r^6$ interactions, and we locate and characterize the points along the commensurate lines where the transition out of the period 3 and 4 phases is conformal. We confirm that it is 3-state Potts for the period-3 phase, and we show that it is Ashkin-Teller with $\nu\simeq 0.80$ for the period-4 phase. We further show that close to these points the transition is still continuous, but with a completely different scaling of the wave-vector, in agreement with a chiral transition. Finally, we propose to use the conformal points as benchmarks for Kibble-Zurek experiments, defining a roadmap towards a conclusive identification of the chiral universality class.