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arXiv:2304.08484 · Physical review. B./Physical review. B

Critical lines and ordered phases in a Rydberg-blockade ladder

Luisa Eck, Paul Fendley

Published Sep 21, 2023• 19 citations
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Abstract

Arrays of Rydberg atoms in the blockade regime realize a wealth of strongly correlated quantum physics, but theoretical analysis beyond the chain is rather difficult. Here we study a tractable model of Rydberg-blockade atoms on the square ladder with a ${\mathbb{Z}}_{2}\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{\mathbb{Z}}_{2}$ symmetry and at most one excited atom per square. We find ${D}_{4}$, ${\mathbb{Z}}_{2}$, and ${\mathbb{Z}}_{3}$ density-wave phases separated by critical and first-order quantum phase transitions. A noninvertible remnant of $U(1)$ symmetry applies to our full three-parameter space of couplings, and its presence results in a larger critical region as well as two distinct ${\mathbb{Z}}_{3}$-broken phases. Along an integrable line of couplings, the model exhibits a self-duality that is spontaneously broken along a first-order transition. Aided by numerical results, perturbation theory, and conformal field theory, we also find critical ${\mathrm{Ising}}^{2}$ and three-state Potts transitions, and provide good evidence that the latter can be chiral.

DOI
10.1103/physrevb.108.125135

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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 Z3{\mathbb{Z}}_{3}Z3​ 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 Z3{\mathbb{Z}}_{3}Z3​ 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 zzz 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.
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