TY - JOUR
T1 - Lifshitz point at commensurate melting of chains of Rydberg atoms
AU - Chepiga, Natalia
AU - Mila, Frédéric
PY - 2021
Y1 - 2021
N2 - 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 p2/8=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.
AB - 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 p2/8=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.
UR - http://www.scopus.com/inward/record.url?scp=85115899313&partnerID=8YFLogxK
U2 - 10.1103/PhysRevResearch.3.023049
DO - 10.1103/PhysRevResearch.3.023049
M3 - Article
AN - SCOPUS:85115899313
SN - 2643-1564
VL - 3
JO - Physical Review Research
JF - Physical Review Research
IS - 2
M1 - 023049
ER -