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We propose the construction of a many-body phase of matter with fractal structure using arrays of Rydberg atoms. The degenerate low energy excited states of this phase form a self-similar fractal structure. This phase is analogous to the so-called type-II fracton topological states. The main challenge in realizing fracton-like models in standard condensed matter platforms is the creation of multi-spin interactions, since realistic systems are typically dominated by two-body interactions. In this work, we demonstrate that the Van der Waals interaction and experimental tunability of Rydberg-based platforms enable the simulation of exotic phases of matter with fractal structures, and the study of a quantum phase transition involving a fractal ordered phase.
Quantum spin ice represents a paradigmatic example on how the physics of frustrated magnets is related to gauge theories. In the present work we address the problem of approximately realizing quantum spin ice in two dimensions with cold atoms in opti
The interplay between antiferromagnetic interaction and hole motion is capable of inducing intriguing conducting topological Haldane phases described by a finite non-local string order parameter. Here we show that these states of matter are captured
We analyze the zero-temperature phases of an array of neutral atoms on the kagome lattice, interacting via laser excitation to atomic Rydberg states. Density-matrix renormalization group calculations reveal the presence of a wide variety of complex s
We numerically study the dynamics after a parameter quench in the one-dimensional transverse-field Ising model with long-range interactions ($propto 1/r^alpha$ with distance $r$), for finite chains and also directly in the thermodynamic limit. In non
Anyons are mainly studied and considered in two spatial dimensions. For fractals, the scaling dimension that characterizes the system can be non integer and can take values between that of a standard one-dimensional or two-dimensional system. Generat