Critical lines and ordered phases in a Rydberg-blockade ladder
Luisa Eck, Paul Fendley
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.