On tensor network representations of the (3+1)d toric code

Abstract

We define two dual tensor network representations of the (3+1)d toric code ground state subspace. These two representations, which are obtained by initially imposing either family of stabilizer constraints, are characterized by different virtual symmetries generated by string-like and membrane-like operators, respectively. We discuss the topological properties of the model from the point of view of these virtual symmetries, emphasizing the differences between both representations. In particular, we argue that, depending on the representation, the phase diagram of boundary entanglement degrees of freedom is naturally associated with that of a (2+1)d Hamiltonian displaying either a global or a gauge ${\mathbb{Z}}_2$-symmetry.

References in corpus (20)

• Non-Abelian Anyons and Topological Quantum Computation
• Generalized Global Symmetries
• Condensate induced transitions between topologically ordered phases
• Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
• Entanglement and topological entropy of the toric code at finite temperature
• Topological order in a 3D toric code at finite temperature
• Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
• Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• Fusion 2-categories and a state-sum invariant for 4-manifolds
• Ground State Degeneracy of Topological Phases on Open Surfaces
• Bulk Anyons as Edge Symmetries: Boundary Phase Diagrams of Topologically Ordered States
• Matrix product operator symmetries and intertwiners in string-nets with domain walls
• Universal Topological Data for Gapped Quantum Liquids in Three Dimensions and Fusion Algebra for Non-Abelian String Excitations
• Fermionic projected entangled-pair states and topological phases
• On 2-form gauge models of topological phases
• Tensor Networks with a Twist: Anyon-permuting domain walls and defects in PEPS
• Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases
• On the stability of topological order in tensor network states
• Energy density of variational states

Cited by in corpus (6)

• Dualities in one-dimensional quantum lattice models: symmetric Hamiltonians and matrix product operator intertwiners
• Long-range entanglement from measuring symmetry-protected topological phases
• Tensor network approach to electromagnetic duality in (3+1)d topological gauge models
• On the stability of topological order in tensor network states
• Boundary and domain wall theories of 2d generalized quantum double model
• Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks