Interplay of localization and topology in disordered dimerized array of Rydberg atoms

TL;DR

This work investigates a disordered, dimerized long-range XY chain inspired by Rydberg tweezer experiments, focusing on how positional disorder and dimerization drive ergodicity breaking beyond standard MBL. Using exact diagonalization, POLFED, and real-space renormalization group methods for excited states (RSRG-X), it reveals an ergodicity-breaking regime characterized by Hilbert-space fragmentation and partial spin-glass order, even in the absence of $ZZ$ interactions. A significant fraction of excited states exhibit symmetry-protected topological (SPT) character across the spectrum, detectable via disconnected entropies and supported by RG-X analysis showing edge and bulk topological structures. Time-dependent studies confirm RG-X predictions: quench dynamics display edge–bulk topological oscillations with system-size–dependent periods, offering experimentally accessible signatures in Rydberg platforms. Together, the results connect localization, topology, and fragmentation in a tunable, realistic model, with implications for experiments and for understanding non-MBL ergodicity in long-range interacting systems.

Abstract

Rydberg tweezer arrays provide a platform for realizing spin-1/2 Hamiltonians with long-range tunneling that decays as a power law with distance. We numerically investigate the effects of positional disorder and dimerization on the properties of excited states in such a one-dimensional system. Our model allows for continuous tuning of both the dimerization pattern and the disorder strength. Within the parameter space constrained by our geometry, we show that both mechanisms lead to a localized phase that does not resemble standard MBL. This phase can be understood as an ensemble of distinct Hilbert space fragmented realizations induced by small inter-spin separations. As dimerization is commonly associated with Symmetry Protected Topological (SPT) physics, we also examine the SPT states across the entire energy spectrum. Despite a partial spin-glass order, we argue that the system hosts an extensive fraction of SPT states.

Figures (17)

• Figure 1: The qualitative phase diagram for the model in $\delta,W$ space where $\delta$ is the dimerization parameter in the model defined by \ref{['eq:model']} and \ref{['eq:pos']} and $W$ is the positional disorder strength. The ergodic domain at low $W,|\delta|$ is surrounded by a localized region characterized by Hilbert space fragmentation (HSF). The bottom panels visualize spin positions for different dimerization, $\delta$.
• Figure 2: Half-chain entanglement entropy $S_{ent}/S^P$ normalized by the Page value (a) and the mean gap ratio $\braket{r_n}$ (b) as a function of the disorder strength $W$ and the dimerization, $\delta$. The ergodic area in the middle, for $\delta>0$, is surrounded by localized regions characterized by low entanglement entropy as well as mean gap ratio being Poissonian or even strongly sub-Poissonian close to borders of the space of parameters.
• Figure 3: Half-chain entanglement entropy $S_{ent}$ and the mean gap ratio $\braket{r_n}$ as a function of the disorder strength $W$ for fixed $\delta = 0$ (a-b) and as a function of dimerization $\delta$ for fixed $W= 0.1$ (c-d).
• Figure 4: Half-chain entanglement entropy $S_{ent}$ and the mean gap ratio $\braket{r_n}$ as a function of the dimerization $\delta$ along the right edge of the parameter space defined via $W=a(1-\delta)/2$ (a-b) and along the left edge, $W=a(1+\delta)/2$ (c-d).
• Figure 5: Normalized gap ratio distributions (a-c), and distributions of the underlying half-chain entanglement entropies of the eigenstates (d-f). Plots (a,d) correspond to the system with $W=0.1, \delta = -0.8$, (b,e) - $W=0.5, \delta = 0.0$, and (c,f) - $W=0.1, \delta = 0.8$. The data correspond to 1000 disorder realizations for $L = 16$. Insets in plots (a) and (c) show the zoomed-in tail behavior of the corresponding gap-ratio distributions.