Numerical investigation of quantum phases and phase transitions in a two-leg ladder of Rydberg atoms
Physical Review Research American Physical Society (APS) 7:1 (2025) 013215
Authors:
Jose Soto-Garcia, Natalia Chepiga
Abstract:
Experiments on chains of Rydberg atoms appear as a 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 interacting via van der Waals potential. We address this problem numerically, using the density matrix renormalization group algorithm. Our results suggest that, quite remarkably,
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
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
Z
k
transition, whose nature depends on
k
. According to our results, the transition into the
Z
2
⊗
Z
̃
2
phase changes its nature multiple times, including an Ashkin-Teller transition that is surprisingly stable over an extended interval, followed by the
Z
4
-chiral transition, and finally in a two step-process mediated melting via the floating phase. The transition into the
Z
3
phase with resonant states on the rungs belongs to the three-state Potts universality class at the commensurate point, to the
Z
3
-chiral Huse-Fisher universality class away from it, and eventually it is through an intermediate floating phase. The Ising transition between
Z
3
and
Z
3
⊗
Z
̃
2
phases, entering the floating phase, opens the possibility to realize lattice supersymmetry in Rydberg quantum simulators.
