Random displacements in critical Rydberg atom arrays

Abstract

Rydberg atom arrays promise high-fidelity quantum simulations of critical phenomena with flexible geometries. Yet experimental realizations inevitably suffer from disorder due to random displacements of atoms, leading to departures from the expected behavior. Here, we study how such positional disorder influences the Ising criticality. Since disorder breaks the $\mathbb{Z}_2$ symmetry, one might expect the system to flow to an infinite-strength disordered fixed point, erasing all nontrivial critical features in low spatial dimensions. Remarkably, we find instead that disorder in Rydberg systems is subjected to nontrivial local constraints, making the physics markedly different from systems with more conventional spatially short-range correlated or long-range correlated disorder. This leads to new classes of criticalities even at dimensions where conventional disorder would destroy criticality altogether. We then demonstrate as a consequence how a novel pseudo-criticality emerges in Rydberg atom chains of experimentally realistic scale, and show that the renormalization group flow is governed by a locally constrained $\mathbb{Z}_2$-breaking perturbation. Our findings uncover new disorder-driven phenomena and underscore the importance of carefully treating disorder effects in quantum simulators.

Figures (3)

• Figure 1: (a) Schematic of a disordered Rydberg atom chain. Each atom is displaced from its designed position by $\delta a_i$, which is randomly distributed. (b) Schematic phase diagram and renormalization group flows of the disordered chain. $\Omega_c$ represents the clean criticality. A random $\partial \phi$ term drives the clean critical system to a novel disordered fixed point (on the $\mathfrak{h}$-axis), but the presence of higher-order random $\phi$ terms makes the system pseudo-critical. That is, the system exhibits key signatures of a critical point over a wide intermediate scale, but is not a true critical point in the infinite-size limit. The three different RG trajectories correspond to varying nearest-neighbor interaction strengths. With stronger interactions, the trajectory detours later.
• Figure 2: Phase boundary of a disordered Rydberg chain for different displacement randomness $\delta a/a\propto\mathfrak{h}$. The interaction term is kept to the first order of $\delta a$ in numerics. Inset shows $\delta \Omega_c \propto \mathfrak{h}^{1/\eta}$ by a log--log scale plot, where $\delta \Omega_c(\mathfrak{h})=\Omega_c(\mathfrak{h})-\Omega_c(\mathfrak{h}=0)$ is the deviation of the critical Rabi frequency from the clean case due to finite disorder. In numerical simulations, we choose $C_6=1.5^6$, $\Delta=1$, and $a=1$.
• Figure 3: $\Delta_\phi$ with different displacement randomness $\delta a/a \propto \mathfrak{h}$ are extracted from two-point functions at finite size $N$. A finite-size scaling form of $\Delta_\phi(\mathfrak{h}, N) = f(\mathfrak{h} N^{3/8})$ is plotted in the main figure.