Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms

TL;DR

The study investigates a quantum Ising model with power-law decaying antiferromagnetic couplings $J_{ij} \propto |\mathbf{r}_i-\mathbf{r}_j|^{-6}$ on amorphous 2D Rydberg arrays to assess spin-glass physics. Using unbiased quantum Monte Carlo with two-replica overlaps, the authors identify a quantum phase transition from a paramagnetic to a spin-glass phase at a critical transverse field $\Gamma_c \approx 0.86$, accompanied by short-range, isotropic antiferromagnetic correlations in the spin-glass phase and a nontrivial spin-overlap distribution $P(q)$ at feasible system sizes. A detailed finite-size scaling analysis yields $b_q \approx 1.63$ and $1/\nu \approx 1.22$, consistent with 2D Edwards-Anderson universality within error bars, while comparisons to the periodic kagome lattice show no glassy order, underscoring the importance of positional disorder. These findings suggest a feasible route to experimentally realize and study quantum spin-glass physics in amorphous Rydberg arrays and illuminate the interplay between disorder and frustration in quantum magnets.

Abstract

The experiments performed with neutral atoms trapped in optical tweezers and coherently coupled to the Rydberg state allow quantum simulations of paradigmatic Hamiltonians for quantum magnetism. Previous studies have focused mainly on periodic arrangements of the optical tweezers, which host various spatially ordered magnetic phases. Here, we perform unbiased quantum Monte Carlo simulations of the ground state of quantum Ising models for amorphous arrays of Rydberg atoms. These models are designed to feature well-controlled local structural properties in the absence of long-range order. Notably, by determining the Edwards-Anderson order parameter, we find evidence of a quantum phase transition from a paramagnetic to a spin-glass phase. The magnetic structure factor indicates short-range isotropic antiferromagnetic correlations. For the feasible sizes, the spin-overlap distribution features a nontrivial structure with two broad peaks and a sizable weight at zero overlap. The comparison against results for the clean kagome lattice, which features local structural properties similar to those of our amorphous arrays, highlights the important role of the absence of long-range structural order of the underlying array. Our findings indicate a route to experimentally implement the details of a Hamiltonian which hosts a quantum spin-glass phase.

Figures (7)

• Figure 1: Panels (a) and (b): representation of a 2D amorphous array (a) and of the kagome lattice (b). Segments connect nearest-neighbor atoms. Panel (c): probability distribution of bond-angle $\theta$ in the amorphous arrays. The vertical lines denote the angles of the kagome lattice (continuous lines) and of the square lattice (dashed line), with periodic boundary conditions.
• Figure 2: Panels (a) and (b): magnetic structure factor $S(\mathbf{k})$ versus $k_x$ and $k_y$, with $\mathbf{k}=(k_x,k_y)$, for (ensemble-averaged) amorphous arrays (a) and for the periodic kagome lattice (b). In panel (b), the (white) hexagons represent the Brillouin zones.
• Figure 3: Main panel: rescaled (disordered averaged) EA order parameter $\left[\left<q^2\right>\right]L^{b_q}$ as a function of the transverse field $\Gamma$. Different datasets correspond to different system sizes. Inset: universal collapse of $\left[\left<q^2\right>\right]L^{b_q}$ plotted as a function of the transverse field $\left(\Gamma-\Gamma_c\right)L^{1/\nu}$. The critical parameters $\Gamma_c$, $1/\nu$, and $b_q$ are obtained by optimizing the data collapse melchert2009autoscalepy, excluding the data shown as empty symbols.
• Figure 4: Distribution of the replica spin-overlap distribution $P(q)$ for the (ensemble averaged) amorphous arrays (left vertical axis) and for the kagome lattice (right vertical axis). Different datasets correspond to different sizes $L$. The transverse field is $\Gamma=0.67<\Gamma_c$.
• Figure S1: Example of patch extraction. Points in light blue represent the entire amorphous array created with the algorithm described in Ref. juliafarre2024amorphous. The black crosses are the centroids identified by K-means clustering performed on the coordinates. The colored clusters are the five patches of $N=100$ atoms each. The zoom shows the detail of the blue patch.