Abstract
AbstractWe consider symmetry-protected topological phases with on-site finite groupGsymmetry$\beta $for two-dimensional quantum spin systems. We show that they have$H^{3}(G,{\mathbb T})$-valued invariant.
Highlights
For each subset Γ of Z2, we denote the set of all finite subsets in Γ by SΓ
For finite Λ, the algebra AΛ can be regarded as the set of all bounded operators acting on the Hilbert space z ∈Λ Cd
For an infinite subset Γ ⊂ Z2, AΓ is given as the inductive limit of the algebras AΛ with Λ ∈ SΓ
Summary
CbΦ := sup sup Φ (X; s) + Φ (X; s) < ∞. 7. There exists 0 < η < 1 satisfying the following: Set ζ (t) := e−t η. This additional condition is the existence of the set of automorphisms which (i) do not move the state and (ii) are almost like β-action restricted to the upper half-plane, except for some 1-dimensional perturbation. From the construction to follow, one can see that the group structure of H3(G, T), which is a simple pointwise multiplication, shows up when we tensor two systems
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