Rényi-like entanglement probe of the chiral central charge

We propose a ground state entanglement probe for gapped, two-dimensional quantum many-body systems that involves taking powers of reduced density matrices in a particular geometric configuration. This quantity, which we denote by ω_α,β, is parameterized by two positive real numbers α, β, and can be seen as a "Rényi-like" generalization of the modular commutator - another entanglement probe proposed as a way to compute the chiral central charge from a bulk wave function. We obtain analytic expressions for ω_α,β for gapped ground states of non-interacting fermion Hamiltonians as well as ground states of string-net models. In both cases, we find that ω_α,β takes a universal value related to the chiral central charge. For integer values of α and β, our quantity ω_α,β can be expressed as an expectation value of permutation operators acting on an appropriate replica system, providing a natural route to measuring ω_α,β in numerical simulations and potentially, experiments.