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We investigate the nature of the phase transitions in the quantumAshkin-Teller chain in the presence of chiral perturbations. We locate theLifshitz line separating a region of direct chiral transitions from the regionwhere the transition is through an intermediate floating phase. Furthermore, weidentify a small region in the vicinity of the four-state Potts point wherechiral perturbations are irrelevant and where the transition remains conformal.Implications to Rydberg atoms experiments are briefly discussed.

Critical properties of the quantum Ashkin-Teller chain with chiral perturbations