Detection of a R\'enyi Index Dependent Transition in Entanglement Entropy Scaling

Abstract

The scaling of entanglement with subsystem size encodes key information about phases and criticality, but the von Neumann entropy is costly to access in experiments and simulations, often requiring full state tomography. The second R\'enyi entropy is readily measured using two-copy protocols and is often used as a proxy for the von Neumann entanglement entropy, where it is assumed to track its asymptotic scaling. Sugino and Korepiny (Int. J. Mod. Phys. B 32, 1850306 (2018)) revealed that in the ground state of some highly constrained spin models, the scaling of the von Neumann and \ren entropies can differ, varying from power law to logarithmic scaling as a function of the \ren index. Here, we construct a number-conserving many-body state that demonstrates a R\'enyi-index-dependent change in the leading entanglement scaling, generalizing previous results to the case of interacting fermions. We introduce a symmetry-aware lower bound on the von Neumann entropy built from charge-resolved R\'enyi entropies that can provide a protocol for diagnosing anomalous entanglement scaling from experimentally accessible data.