The recent investigation of chains of Rydberg atoms has brought back the problem of commensurate-incommensurate transitions into the focus of current research. In two-dimensional classical systems or in one-dimensional quantum systems, the commensurate melting of a period-$p$ phase with $p$ larger than 4 is known to take place through an intermediate floating phase where correlations between domain walls or particles decay only as a power law, but when $p$ is equal to 3 or 4, it has been argued by Huse and Fisher that the transition could also be direct and continuous in a nonconformal chiral universality class with a dynamical exponent larger than 1. This is only possible, however, if the floating phase terminates at a Lifshitz point before reaching the conformal point, a possibility debated since then. Here we argue that this is a generic feature of models where the number of particles is not conserved because the exponent of the floating phase changes along the Pokrovsky-Talapov transition and can, thus, reach the value at which the floating phase becomes unstable. Furthermore, we show numerically that this scenario is realized in an effective model of the period-3 phase of Rydberg chains in which hard-core bosons are created and annihilated three by three: The Luttinger liquid parameter reaches the critical value $p^2/8=9/8$ along the Pokrovsky-Talapov transition, leading to a Lifshitz point that separates the floating phase from a chiral transition. Implications beyond Rydberg atoms are briefly discussed.

中文翻译：

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Lifshitz指出里德伯格原子链的相应熔化

最近对里德堡原子链的研究使相称过渡转变问题成为当前研究的重点。在二维经典系统或一维量子系统中，周期的相应熔化$p$ 与相 $p$ 大于4的情况是通过中间浮动阶段发生的，在该阶段，畴壁或粒子之间的相关性仅作为幂定律衰减，但是当 $p$等于3或4，Huse和Fisher认为，在动态指数大于1的非保形手性普适性类别中，跃迁也可以是直接和连续的。但是，只有在浮相终止时才有可能在到达共形点之前在Lifshitz点，此后一直在讨论这种可能性。在这里，我们认为这是模型的通用特征，其中的粒子数不守恒，因为浮动相的指数沿Pokrovsky-Talapov跃迁发生变化，因此可以达到浮动相变得不稳定的值。此外，我们用数字显示了这种情况是在Rydberg链的3期阶段的有效模型中实现的，在该模型中创建了硬核玻色子并三三消灭了玻色子：$p^{\mathrm{2个}}/8=9/8$沿着波克罗夫斯基-塔拉波夫（Pokrovsky-Talapov）过渡，到达一个Lifshitz点，该点将浮动相与手性过渡分开。简要讨论了Rydberg原子以外的含义。