Cornering the universal shape of fluctuations

Abstract

Understanding the fluctuations of observables is one of the main goals in science, be it theoretical or experimental, quantum or classical. We investigate such fluctuations when only a subregion of the full system can be observed, focusing on geometries with sharp corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples, including fractional quantum Hall states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with quantum entanglement, extensions to three dimensions, as well as experiments to probe the geometry of fluctuations.

7+7 pages, 2+0 figures. v2: New results regarding the volume and area law terms for general geometries and dimensions

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• Measuring Rényi entanglement entropy with high efficiency and precision in quantum Monte Carlo simulations
• Scaling of disorder operator at deconfined quantum criticality
• Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with $U(1)$ symmetry
• Topological Disorder Parameter
• Universal features of entanglement entropy in the honeycomb Hubbard model
• Multipartite entanglement in two-dimensional chiral topological liquids
• Aspects of N-partite information in conformal field theories
• The entanglement entropy of the quantum Hall edge and its geometric contribution
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Is the EMI model a QFT? An inquiry on the space of allowed entropy functions