QIP2021 | Entanglement bootstrap program (Isaac Kim)

Speaker: Isaac Kim (University of California San Diego | Osaka University | The University of Sydney )

We introduce the entanglement bootstrap program, a powerful new approach to study topologically ordered quantum many-body systems. In this program, we posit that local reduced density matrices of the underlying system obey a set of simple constraints that are motivated by the entanglement entropy calculations in the literature. We show that these constraints lead to a highly nontrivial set of identities that can be interpreted as the basic axioms of the emergent theory describing the topological charges in such systems. The surprising nature of our work lies in the fact that these basic axioms of the emergent theory, which are typically assumed in the literature, can actually be derived from a simple entanglement property of the ground state. Furthermore, we apply this line of reasoning to systems with gapped domain walls and derive a hitherto unknown set of topological charges and identities that those topological charges need to satisfy. Thus, our work establishes a deep connection between entanglement and the exotic behaviors of topological charges in topologically ordered systems.

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