Lifshitz point at commensurate melting of 1D Rydberg atoms

TL;DR

This paper investigates the nature of phase transitions in 1D Rydberg atom chains, revealing a Lifshitz point at the melting of a period-3 phase, which influences the transition's universality class and is relevant for non-conserved particle systems.

Contribution

It demonstrates that Lifshitz points are a generic feature in models with non-conserved particles, specifically in Rydberg chains, and provides numerical evidence for this scenario.

Findings

Identification of a Lifshitz point in Rydberg chains.

The Luttinger parameter reaches critical value at the transition.

The floating phase terminates at the Lifshitz point, affecting transition universality.

Abstract

The recent investigation of chains of Rydberg atoms has brought back the problem of commensurate-incommensurate transitions into the focus of current research. In 2D classical systems, or in 1D 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 non-conformal 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.