From Entanglement Bootstrap to DHR Theory

Abstract: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.

Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech); Operator Algebras (math.OA); Quantum Physics (quant-ph)

arXiv:2610.38821 [math-ph]

(or arXiv:2610.38821v1 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2610.38821 Focus to learn more arXiv-issued DOI via DataCite

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