Renyi-like entanglement measure of the chiral central charge

We introduce a "Renyi-like" entanglement measure for gapped (2+1)D systems, which involves taking powers of reduced density matrices in a particular geometric configuration. From explicit calculations on free fermion ground states, we find that our quantity is equal to a rational number times the real space Chern number. For generic interacting systems, we conjecture that our quantity gives a rational number times the chiral central charge, though fine-tuned examples exist where our quantity takes on spurious values. By taking an appropriate limit one recovers the modular commutator, another entanglement measure proposed to calculate the chiral central charge.