Lifshitz point at commensurate melting of 1D Rydberg atoms

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.

arXiv comment10 pages, 9 figures

References in corpus (15)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Probing many-body dynamics on a 51-atom quantum simulator
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator
• Competing density-wave orders in a one-dimensional hard-boson model
• Numerical study of the chiral ${\mathbb{Z}}_3$ quantum phase transition in one spatial dimension
• Quantum field theory for the chiral clock transition in one spatial dimension
• Phase diagram of the $Z_3$ Parafermionic Chain with Chiral Interactions
• Floating phase versus chiral transition in a 1D hard-boson model
• Critical Exponents of the Chiral Potts Model from Conformal Field Theory
• Kibble-Zurek exponent and chiral transition of the period-4 phase of Rydberg chains
• Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models
• Identifying the Huse-Fisher universality class of the three-state chiral Potts model

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