Seminario Q-Math
Topologically-ordered 2-d quantum phases and the Haag duality property
Ponente: Alberto Ruiz de Alarcón (CUNEF Universidad)Fecha: martes 04 de noviembre de 2025 - 13:00Lugar: Room 2.2.D08, Universidad Carlos III de Madrid
Online: https://eu.bbcollab.com/guest/22f7877a774148a3aee3e398a4a86380 (active on request)
Resumen:
Topologically ordered two-dimensional quantum many-body systems have attracted considerable attention because of their striking emergent phenomena, such as ground-state degeneracy depending on topology, the absence of local order parameters, or long-range entanglement. A particularly important feature is the appearance of quasiparticle excitations with nontrivial braid statistics, called anyons, which are actually expected to classify all non-chiral two-dimensional gapped quantum phases. However, a fully rigorous understanding remains incomplete. A key insight established by Naaijkens is that a strong notion of locality, known as Haag duality, implies the existence of anyons (specifically, that one can derive a C*-braided tensor category for certain equivalence classes of irreducible representations of the quasi-local observable C*-algebra). More recently, Ogata introduced a weaker but phase-stable version, known as approximate Haag duality. An open problem has been to establish this property in quantum spin systems beyond the few known cases: one-dimensional systems and two-dimensional Abelian quantum double models. In this talk, I will present a construction of topologically ordered two-dimensional tensor-network states based on biconnected C*-weak Hopf algebras, which serve as renormalization fixed-point representatives of all known non-chiral phases (i.e. encompassing Levin-Wen string-net models), and sketch a proof of the fact that these states satisfy (approximate) Haag duality. Based on arXiv:2204.05940 and arXiv:2509.23734.
