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arXiv:1806.01867 · Physical Review A

Numerical study of the chiral Z 3 quantum phase transition in one spatial dimension

Rhine Samajdar, Soonwon Choi, Hannes Pichler, Mikhail D. Lukin, Subir Sachdev A

Published Aug 13, 2018• 107 citations
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Abstract

Recent experiments on a one-dimensional chain of trapped alkali-metal atoms [Bernien et al., Nature (London) 551, 579 (2017)] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous ${\mathbb{Z}}_{3}$ symmetry breaking is described by a constrained model of hard-core bosons proposed by Fendley et al. [Phys. Rev. B 69, 075106 (2004)]. By symmetry arguments, the transition is expected to be in the universality class of the ${\mathbb{Z}}_{3}$ chiral clock model with parameters preserving both time-reversal and spatial-inversion symmetries. We study the nature of the order--disorder transition in these models and numerically calculate its critical exponents with exact diagonalization and density-matrix renormalization-group techniques. We use finite-size scaling to determine the dynamical critical exponent $z$ and the correlation length exponent $\ensuremath{\nu}$. Our analysis presents the only known instance of a strongly coupled generic transition between gapped states with $z\ensuremath{\ne}1$, implying an underlying nonconformal critical-field theory.

DOI
10.1103/physreva.98.023614

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