Quantum Matter Seminar- Bowen Shi (UC San Diego)- Emergent Chirality and Conformal Symmetry from a Single Wave Function

Abstract: Chiral topologically ordered systems have a nonzero chiral central charge, which is responsible for a nontrivial thermal Hall conductance at low temperatures. On closed orientable manifolds, the system is gapped, while in the presence of an edge, the edge remains gapless. The gapless edge is robust, which is often believed to have an emergent conformal symmetry. In this talk, we discuss three related things. (1) We discuss a recently proposed formula that extracts the chiral central charge from a single bulk wave function. (2) We define three candidates of "quantum cross ratios" near a chiral edge, defined using information-theoretic quantities, to test if a chiral edge has an emergent conformal symmetry. In our numerics studies on both regular and irregular chiral edges, all three "quantum cross-ratio" candidates are identical with high precision, and they are shown to satisfy the consistency of cross-ratios. We extend the entanglement bootstrap approach to gapless edge, which explains the observation with a small set of assumptions. (3) We use modular flow to construct coherent states (with only edge excitations) and verify the Virasoro algebra acting on such coherent states.