SKM 2023 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
TT: Fachverband Tiefe Temperaturen
TT 48: Topological Superconductors
TT 48.6: Vortrag
Donnerstag, 30. März 2023, 10:45–11:00, HSZ 304
Symmetry enriched entanglement properties of chiral Skyrme insulators — •Joe Winter1,2,3, Bernd Braunecker3, and Ashley Cook1,2 — 1Max Planck Institute for Chemical Physics of Solids, Nothnitzer Straße 40, 01187 Dresden, Germany — 2Max Planck Institute for the Physics of Complex Systems, Nothnitzer Straße 38, 01187 Dresden, Germany — 3SUPA, School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS, UK
The expectation value of an observable O may be computed with a density matrix ρ as Tr( ρ O). In this work, we introduce the symmetry-enriched partial trace operation for density matrices, ρT = TrT( ρ ), a partial trace performed over T degrees of freedom on a density matrix as part of partial computation of an expectation value for an observable O. That is, for representation of observable O after tracing out T being OT, ρT satisfies Tr( ρ O ) = ⟨ O ⟩ = ⟨ OT ⟩ = Tr( ρT OT ), with symmetry-enrichment deriving from differences in symmetry between O and OT. We use this to characterize bulk-boundary correspondence of topological skyrmion phases, by computing the symmetry-enriched reduced density matrix in the 2D bulk of a topological skyrmion phase, and for slab geometries with open boundary conditions in one direction. We show winding of this reduced density matrix matches winding of the spin expectation value vector in the bulk, and the entanglement spectrum of the reduced density matrix for the slab geometry reveals Q topologically-protected, chiral edge modes for skyrmion number Q characterizing the bulk topological skyrmion phase.