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

TL;DR

This paper maps the ground-state phase diagram of Rydberg atoms in a two-leg ladder, revealing complex quantum phase transitions and symmetry-breaking phenomena using numerical DMRG methods.

Contribution

It provides the first detailed numerical analysis of quantum phases and transitions in a two-leg Rydberg atom ladder, uncovering novel symmetry-breaking and universality classes.

Findings

Identification of paired $ ext{Z}_k$ crystalline phases with broken $ ilde{ ext{Z}}_2$ symmetry.

Observation of multiple universality classes including Ising, Ashkin-Teller, and Potts transitions.

Discovery of a floating phase mediating certain phase transitions.

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.