Snapshot renormalization group for quantum matter

Recent advances in quantum simulator experiments enable unprecedented access to quantum many-body states through snapshot measurements of individual many-body configurations. Here, we introduce an exact renormalization group (RG) transformation that can be directly applied to any such snapshot dataset. Our SnapshotRG operates in real space, but can also be directly translated to an RG in the abstract dataspace of measurement configurations, providing a framework for the characterization of quantum many-body systems on a more general level. We demonstrate that snapshot datasets in dataspace exhibit self-similarity at continuous phase transitions, providing an explanation for the recently observed scale-freeness of so-called wavefunction networks. As a consequence, scale invariance extends beyond traditional low-order correlation functions to encompass the full statistical structure of quantum states as contained in their snapshot datasets. Our SnapshotRG can be readily implemented with snapshot data generated by numerical method such as neural quantum states or any quantum simulation platform, offering a versatile tool for characterizing quantum phase transitions and critical phenomena in quantum matter.