Chiral Central Charge from Real-Space Twist Operator Correlator

Recent years have witnessed substantial progress in the entanglement-based characterization of quantum phases of matter, with growing interest in real-space formulas due to their theoretical and experimental relevance. For two-dimensional gapped quantum systems, we propose a universal real-space formula for the chiral central charge based on the twist-operator correlator Z g,h=ψ(N) T A(g) T B(h) T C(g) T C(h) ψ(N), where ψ(N)= ψ N is the N-copy state and g,h in S N are permutations. The twist operator T R(g) permutes the N replicas within region R according to g. For pairs (g,h) satisfying the spherical condition, we show that the phase of the correlator is determined by the chiral central charge c- through Z g,h/ Z g,h =(θ gθ h/θ gh) c-, where θ g c- is the topological spin of the twist defect labeled by g in S N. The construction applies to both bosonic and fermionic systems. We derive the formula within a field-theoretic framework under suitable assumptions and further test it numerically in microscopic lattice models. Our results establish a universal connection between real-space entanglement structures and the chiral central charge, providing a systematic framework for characterizing chiral topological phases directly on the lattice.