Domain walls in topological phases and the Brauer-Picard ring for $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$

Abstract

We show how to calculate the relative tensor product of bimodule categories (not necessarily invertible) using ladder string diagrams. As an illustrative example, we compute the Brauer-Picard ring for the fusion category $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$. Moreover, we provide a physical interpretation of all indecomposable bimodule categories in terms of domain walls in the associated topological phase. We show how this interpretation can be used to compute the Brauer-Picard ring from a physical perspective.

arXiv comment16 pages, 1 figure, 3 tables, comments welcome

References in corpus (27)

• Fault-tolerant quantum computation by anyons
• Topological quantum memory
• String-net condensation: A physical mechanism for topological phases
• Quantum Error Correction for Quantum Memories
• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological Quantum Distillation
• Building logical qubits in a superconducting quantum computing system
• Models for gapped boundaries and domain walls
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• TFT construction of RCFT correlators I: Partition functions
• Higher-dimensional Algebra and Topological Quantum Field Theory
• Implementing a strand of a scalable fault-tolerant quantum computing fabric
• Quantum memories at finite temperature
• Theory of defects in Abelian topological states
• Correspondences of ribbon categories
• Quantum Measurements and Gates by Code Deformation
• Fault-tolerant logical gates in quantum error-correcting codes
• Topological color code and symmetry-protected topological phases
• Gapped boundaries, group cohomology and fault-tolerant logical gates
• The boundaries and twist defects of the color code and their applications to topological quantum computation
• Universal Quantum Computation with Gapped Boundaries
• The blob complex
• The Karoubi envelope and Lee's degeneration of Khovanov homology
• On the Brauer groups of symmetries of abelian Dijkgraaf-Witten theories
• Tensor Networks with a Twist: Anyon-permuting domain walls and defects in PEPS
• Entropic Barriers for Two-Dimensional Quantum Memories
• Fusing Binary Interface Defects in Topological Phases: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ case

Cited by in corpus (13)

• Matrix product operator symmetries and intertwiners in string-nets with domain walls
• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Topological aspects of the critical three-state Potts model
• Composing topological domain walls and anyon mobility
• Computing data for Levin-Wen with defects
• Fusing Binary Interface Defects in Topological Phases: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ case
• Higher-group symmetry of (3+1)D fermionic ${\mathbb{Z}}_2$ gauge theory: logical CCZ, CS, and T gates from higher symmetry
• Bulk-to-boundary anyon fusion from microscopic models
• Computing Defects Associated to Bounded Domain Wall Structures: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ Case
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Gauging Defects in Quantum Spin Systems
• Revisiting the symmetry-resolved entanglement for non-invertible symmetries in $1+1$d conformal field theories
• Weak Hopf tube algebra for domain walls between 2d gapped phases of Turaev-Viro TQFTs