Fusion of one-dimensional gapped phases and their domain walls

Abstract

Finite depth quantum circuits provide an equivalence relation between gapped phases. Moreover, there can be nontrivial domain walls either within the same gapped phase or between different gapped phases, whose equivalence relations are given by finite depth quantum circuits in one lower dimension. In this paper, we use such unitary equivalence relations to study the fusion of one-dimensional gapped phases. In particular, we use finite depth circuits to fuse two gapped phases, local unitaries to fuse two domain walls, and a combination of both to fuse gapped phases with domain walls. This provides a concrete illustration of some simple aspects of the `higher-category' structure of gapped defects in a higher-dimensional trivial gapped bulk state.

References in corpus (25)

• Anyons in an exactly solved model and beyond
• Unpaired Majorana fermions in quantum wires
• Persistent entanglement in arrays of interacting particles
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Topological phases of fermions in one dimension
• Classifying quantum phases using Matrix Product States and PEPS
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• On finite symmetries and their gauging in two dimensions
• PEPS as ground states: degeneracy and topology
• Non-Invertible Duality Defects in 3+1 Dimensions
• Higher Gauging and Non-invertible Condensation Defects
• Non-Invertible Higher-Categorical Symmetries
• Topological Defects on the Lattice I: The Ising model
• On the classification of topological orders
• Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
• Unifying Constructions of Non-Invertible Symmetries
• Topological order in 1D Cluster state protected by symmetry
• Quantum circuit complexity of one-dimensional topological phases
• Sequential Quantum Circuits as Maps between Gapped Phases
• Categories of quantum liquids I
• One dimensional gapped quantum phases and enriched fusion categories
• Defects in the 3-dimensional toric code model form a braided fusion 2-category

Cited by in corpus (5)

• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
• Fusion of Low-Entanglement Excitations in 2D Toric Code
• Condensation Completion and Defects in 2+1D Topological Orders
• Quantum Monte Carlo and Stabilizer States