Strict area law entanglement versus chirality

A quantum many-body state in two spatial dimensions may exhibit robust chirality, which can manifest through non-vanishing thermal or electric Hall conductance. In this talk, we present two no-go theorems that forbid a quantum state from having both such robust chirality and strict area-law entanglement entropies in a Hilbert space with finite local dimensions. As a crucial ingredient in the proofs, we introduce a novel quantum information-theoretic primitive called instantaneous modular flow, which has many other potential applications.