Quantum critical properties of rydberg arrays in and out of equilibrium

Abstract

Rydberg atoms trapped in optical tweezers have emerged as a powerful platform for exploring the physics of low-dimensional systems. Thanks to the precise control over the tweezers location, interatomic interactions, and couplings to external fields, these platforms have revealed a wide variety of critical phenomena.

This thesis numerically explores the quantum phases and phase transitions that can be engineered in quasi one-dimensional arrays of Rydberg atoms. It employs a combination of equilibrium and non-equilibrium approaches within the matrix product state framework.

We first studied the quantum Kibble–Zurek (KZ) mechanism in minimal one-dimensional models, showing how boundary conditions and quench endpoints affect scaling behavior. A refined definition of kinks was introduced, yielding robust results even away from the classical Hamiltonian. Building on this, we incorporated a blockade model into the time-evolving block decimation (TEBD) algorithm and combined KZ with finite time scaling (FTS) to study Rydberg chains, establishing a protocol suitable for experiments. This approach distinguished the Kosterlitz–Thouless transition from the Huse–Fisher universality class, providing an alternative way to experimentally detect the floating phase, and allowed the precise location of conformal points as well as the extraction of critical exponents.

Motivated by optical tweezer imperfections, we then examined the effect of disorder on the critical phenomena observed in these chains. We found that disorder alters the nature of quantum criticality, driving the system toward the infinite-disorder universality class, and visibly changing the nature of the KZ scaling. It also localizes the algebraic correlations of the floating phase, destroying Friedel oscillations in the bulk of the chain and saturating the entanglement entropy at a finite value.

Finally, we extended the analysis to two-leg Rydberg ladders, where the phase diagram revealed new phases with resonant Rydberg states between the upper and lower chains. This geometry produced novel critical phenomena, including the merging of two Ising transitions into the Ashkin–Teller universality class and the more exotic merging of an Ising and Pokrovsky–Talapov transition.

The findings presented here provide a theoretical guidance for investigating critical dynamics, the impact of disorder, and the emergence of exotic critical phenomena in both one and quasi-two-dimensional Rydberg atom arrays.