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arXiv:1907.12511 · Physical Review Letters

Anomalous Diffusion and Localization in a Positionally Disordered Quantum Spin Array

Raphaël Menu, Tommaso Roscilde

Published Apr 2, 2020• 17 citations
arXivHTMLPDF

Abstract

Disorder in quantum systems can lead to the disruption of long-range order in the ground state and to the localization of the elementary excitations. Here we exhibit an alternative paradigm, by which disorder preserves long-range order in the ground state, while it localizes the elementary excitations above it, introducing a stark dichotomy between static properties-mostly sensitive to the density of states of excitations-and nonequilibrium dynamical properties-sensitive to the spatial structure of excitations. We exemplify this paradigm with a positionally disordered 2d quantum Ising model with r^{-6} interactions, capturing the internal-state physics of Rydberg-atom arrays. Disorder is found to lead to multifractality and localization of the spin-wave excitations above a ferromagnetic ground state; as a result, the spreading of entanglement and correlations starting from a factorized state exhibits anomalous diffusion with a continuously varying dynamical exponent, interpolating between ballistic and arrested transport. Our findings are directly relevant for the low-energy dynamics in quantum simulators of quantum Ising models with power-law decaying interactions.

DOI
10.1103/physrevlett.124.130604

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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.
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