Remote detectability from entanglement bootstrap I: Kirby's torus trick

Abstract

Remote detectability is often taken as a physical assumption in the study of topologically ordered systems, and it is a central axiom of mathematical frameworks of topological quantum field theories. We show under the entanglement bootstrap approach that remote detectability is a necessary property; that is, we derive it as a theorem. Starting from a single wave function on a topologically-trivial region satisfying the entanglement bootstrap axioms, we can construct states on closed manifolds. The crucial technique is to immerse the punctured manifold into the topologically trivial region and then heal the puncture. This is analogous to Kirby's torus trick. We then analyze a special class of such manifolds, which we call pairing manifolds. For each pairing manifold, which pairs two classes of excitations, we identify an analog of the topological $S$-matrix. This pairing matrix is unitary, which implies remote detectability between two classes of excitations. These matrices are in general not associated with the mapping class group of the manifold. As a by-product, we can count excitation types (e.g., graph excitations in 3+1d). The pairing phenomenon occurs in many physical contexts, including systems in different dimensions, with or without gapped boundaries. We provide a variety of examples to illustrate its scope.

110+20 pages. Many figures

References in corpus (16)

• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Higher Gauging and Non-invertible Condensation Defects
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding
• Braided fusion categories, gravitational anomalies, and the mathematical framework for topological orders in any dimensions
• Universal tripartite entanglement in one-dimensional many-body systems
• Short-range entanglement and invertible field theories
• Universal Topological Data for Gapped Quantum Liquids in Three Dimensions and Fusion Algebra for Non-Abelian String Excitations
• General procedure for determining braiding and statistics of anyons using entanglement interferometry
• Composing topological domain walls and anyon mobility
• Gapped boundaries of (3+1)d topological orders
• Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point
• Detecting topological order from modular transformations of ground states on the torus
• Extracting Wilson loop operators and fractional statistics from a single bulk ground state
• Immersed figure-8 annuli and anyons

Cited by in corpus (1)

• Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter