Anyon condensation and a generic tensor-network construction for symmetry protected topological phases

Abstract

We present systematic constructions of tensor-network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries. From the classification point of view, our results show that in spatial dimensions $d=1,2,3$, the cohomological bosonic SPT phases protected by a general symmetry group $SG$ involving onsite and spatial symmetries are classified by the cohomology group $H^{d+1}(SG,U(1))$, in which both the time-reversal symmetry and mirror reflection symmetries should be treated as anti-unitary operations. In addition, for every SPT phase protected by a discrete symmetry group and some SPT phases protected by continous symmetry groups, generic tensor-network wavefunctions can be constructed which would be useful for the purpose of variational numerical simulations. As a by-product, our results demonstrate a generic connection between rather conventional symmetry enriched topological phases and SPT phases via an anyon condensation mechanism.

34 pages, 13 figures. Add figures, references updated

References in corpus (19)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Crystalline Insulators
• "Deconfined" quantum critical points
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• A classification of symmetry enriched topological phases with exactly solvable models
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Explicit tensor network representation for the ground states of string-net models
• Gauging quantum states: from global to local symmetries in many-body systems
• Implementing global Abelian symmetries in projected entangled-pair state algorithms
• Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
• Exact entanglement renormalization for string-net models
• Chiral projected entangled-pair state with topological order
• Symmetries and boundary theories for chiral Projected Entangled Pair States
• Topological Phases Protected By Reflection Symmetry and Cross-cap States
• Bridging Fermionic and Bosonic Short Range Entangled States

Cited by in corpus (1)

• Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices