Dr. Natalia Chepiga

Abstract:

Quantum phase transitions are characterized by the universal scaling laws in the critical region surrounding the transitions. This universality is also manifested in the critical real-time dynamics through the quantum Kibble-Zurek mechanism. In recent experiments on a Rydberg atom quantum simulator, the Kibble-Zurek mechanism was used to probe the nature of quantum phase transitions. In this paper, we analyze the caveats associated with this method and develop strategies to improve its accuracy. Focusing on two minimal models—transverse-field Ising and quantum three-state Potts, both in one dimension—we study the effect of boundary conditions, the location of the endpoints, and some subtleties in the definition of the kink operators. In particular, we show that the critical scaling of the most intuitive types of kinks is extremely sensitive to the correct choice of endpoint, while more advanced types of kinks exhibit remarkably robust universal scaling. Furthermore, we show that when kinks are tracked over the entire chain, fixed boundary conditions improve the accuracy of the scaling. Surprisingly, the Kibble-Zurek critical scaling appears to be equally accurate whether the fixed boundary conditions are chosen to be symmetric or antisymmetric. We also show that the density of kinks extracted in the central part of long chains obeys the predicted universal scaling for all types of boundary conditions. Finally, we test our kink definition for the Ising transition on the period-2 phase of the Rydberg model and show that it is more robust against the endpoint than the standard definition.

Abstract:

Chains of Rydberg atoms have emerged as a powerful platform for exploring low-dimensional quantum physics. This success originates from the precise control of lattice geometries provided by optical tweezers, which allows access to a wide range of synthetic quantum phases. Experiments on one-dimensional arrays have stimulated tremendous progress in understanding quantum phase transitions into crystalline phases. However, the finite width of tweezers introduces small variations in interatomic distances, leading to quenched disorder in the interactions. In this Letter, we numerically study how such disorder alters the nature of two critical regimes observed in experiments. First, following experimental protocols, we analyze Kibble-Zurek dynamics and find a crossover from the clean Ising transition to the infinite-randomness fixed point as system size and disorder strength increase. Second, we show that the floating phase-an incommensurate Luttinger liquid phase emerging at stronger interactions-is localized by the disorder, yet preserves short-range incommensurate correlations with the same leading wave vector. Our results clearly reveal an additional conceptual challenge in understanding critical phenomena using Rydberg-based quantum simulators.

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.