From Entanglement Bootstrap to DHR Theory

Speaker: Yoshiko Ogata (Kyoto University)
Series: Isaac Newton Institute Seminar Series
Note: MMBW03 - Structure of entanglement

We establish a direct connection between the entanglement bootstrap and the
Doplicher--Haag--Roberts theory of superselection sectors for two-dimensional
quantum spin systems. Under the entanglement-bootstrap assumptions, we prove
Haag duality and establish a one-to-one correspondence between simple
entanglement-bootstrap anyon types and irreducible superselection sectors. For
each fusion channel, we further construct an affine bijection from density
matrices on the entanglement-bootstrap fusion space to normalized positive
intertwiners in the corresponding operator-algebraic fusion channel. These
results connect the entropic and operator-algebraic descriptions of anyons
directly, without passing through exactly solvable lattice models.This is a joint work with Kohtaro Kato.