Kavli Affiliate: Natalia Chepiga
| First 5 Authors: Jose Soto Garcia, Natalia Chepiga, , ,
| Summary:
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 $mathbb{Z}_2otimes tilde{mathbb{Z}}_2$
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 $mathbb{Z}_3otimes
tilde{mathbb{Z}}_2$ phases, coming across the floating phase, opens the
possibility to realize lattice supersymmetry in Rydberg quantum simulators.
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