Correlator method for multi-entropy calculation in fermion gaussian systems

Multi-entropy is a quantum information theoretical quantity proposed to capture multi-partite entanglement in pure states. We focus on the multi-entropy for tripartition, and develop the correlator method, which expresses this multi-entropy in terms of correlation functions, for fermion Gaussian states. The correlator method is applied to numerically evaluate multi-entropy for free fermion systems such as Chern insulators. The calculation provides evidence that for gapped ground states in (2+1)-dimensional topological liquids, the difference between multi-entropy for tripartition and second Rényi entropies is bounded from below by (c_tot/4)ln2 where c_tot is the central charge of ungappable degrees of freedom.