Critical lines and ordered phases in a Rydberg-blockade ladder

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 ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ 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 non-invertible 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 Ising${}^2$ and three-state Potts transitions, and provide good evidence that the latter can be chiral.

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Cited by in corpus (9)

• From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects
• Tunable quantum criticality in multicomponent Rydberg arrays
• Numerical investigation of quantum phases and phase transitions in a two-leg ladder of Rydberg atoms
• Global symmetries of quantum lattice models under non-invertible dualities
• Critical behavior of lattice gauge theory Rydberg simulators from effective Hamiltonians
• Adiabatic echo protocols for robust quantum many-body state preparation
• Phase diagram of Rydberg atoms in a two-leg rectangular ladder
• Dualities between 2+1d fusion surface models from braided fusion categories
• Analogs of deconfined quantum criticality for non-invertible symmetry breaking in 1d