“Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids” Published in Proceedings of the National Academy of Sciences

Pictured are (left) a quantum spin liquid (QSL) phase and (right) its structure factor (proportional to the scattering intensity in the scattering experiments). Chen et al. unveiled a hidden structural property of classical and quantum spin liquids known as hyperuniformity (i.e., infinite-wavelength density fluctuations are anomalously suppressed in these systems), and discovered new metrics that can distinguish a quantum spin liquid phase from other proximate quantum phases. Their findings may help identify potential QSL candidates, and represent the first example of the emergence of disordered hyperuniformity in strongly correlated, long-range entangled quantum systems.

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Classical spin liquids (CSLs) are intriguing states of matter that do not exhibit long-range magnetic order and are characterized by an extensive ground-state degeneracy. Adding quantum fluctuations, which induce dynamics between these different classical ground states, can give rise to quantum spin liquids (QSLs). QSLs are highly entangled quantum phases of matter characterized by fascinating emergent properties, such as fractionalized excitations and topological order. One such exotic quantum liquid is the \(\mathbb{Z}_2\) QSL, which can be regarded as a resonating valence bond (RVB) state formed from superpositions of dimer coverings of an underlying lattice. In this work, we unveil a hidden large-scale structural property of archetypal CSLs and QSLs known as hyperuniformity, i.e., normalized infinite-wavelength density fluctuations are completely suppressed in these systems. In particular, we first demonstrate that classical ensembles of close-packed dimers and their corresponding quantum RVB states are perfectly hyperuniform in general. Subsequently, we focus on a ruby-lattice spin liquid that was recently realized in a Rydberg-atom quantum simulator, and show that the QSL remains effectively hyperuniform even in the presence of a finite density of spinon and vison excitations, as long as the dimer constraint is still largely preserved. Moreover, we demonstrate that metrics based on the framework of hyperuniformity can be used to distinguish the QSL from other proximate quantum phases. These metrics can help identify potential QSL candidates, which can then be further analyzed using more advanced, computationally intensive quantum numerics to confirm their status as true QSLs.