Numerical investigation of quantum phases and phase transitions in a two-leg ladder of Rydberg atoms

Abstract

Experiments on chains of Rydberg atoms appear as a new playground to study quantum phase transitions in 1D. As a natural extension, we report a quantitative ground-state phase diagram of Rydberg atoms arranged in a two-leg ladder that interact via van der Waals potential. We address this problem numerically, using the Density Matrix Renormalization Group (DMRG) algorithm. Our results suggest that, surprisingly enough, ${\mathbb{Z}}_k$ crystalline phases, with the exception of the checkerboard phase, appear in pairs characterized by the same pattern of occupied rungs but distinguishable by a spontaneously broken ${\tilde{\mathbb{Z}}}_2$ symmetry between the two legs of the ladder. Within each pair, the two phases are separated by a continuous transition in the Ising universality class, which eventually fuses with the ${\mathbb{Z}}_k$ transition, whose nature depends on $k$. According to our results, the transition into the ${\mathbb{Z}}_2\otimes {\tilde{\mathbb{Z}}}_2$ phase changes its nature multiple of times and, over extended intervals, falls first into the Ashkin-Teller, latter into the ${\mathbb{Z}}_4$-chiral universality class and finally in a two step-process mediated by a floating phase. The transition into the ${\mathbb{Z}}_3$ phase with resonant states on the rungs belongs to the three-state Potts universality class at the commensurate point, to the ${\mathbb{Z}}_3$-chiral Huse-Fisher universality class away from it, and eventually it is through an intermediate floating phase. The Ising transition between ${\mathbb{Z}}_3$ and ${\mathbb{Z}}_3\otimes {\tilde{\mathbb{Z}}}_2$ phases, coming across the floating phase, opens the possibility to realize lattice supersymmetry in Rydberg quantum simulators.

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Cited by in corpus (9)

• Tricritical Kibble-Zurek scaling in Rydberg atom ladders
• Lattice Defects in Rydberg Atom Arrays
• Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms
• Adiabatic echo protocols for robust quantum many-body state preparation
• Phase diagram of Rydberg atoms in a two-leg rectangular ladder
• Dynamics of antiferromagnetic Dimers in Rydberg Atom Chains
• Rydberg Atoms in a Ladder Geometry: Quench Dynamics and Floquet Engineering
• Extended Ashkin-Teller transition in two coupled frustrated Haldane chains
• Quantum criticality and factorization in a constrained Rydberg spin chain