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Entanglement renormalization is a real-space renormalization group (RG) transformation for quantum many-body systems.
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The present discussion can be generalized to states that transform under ( V ^ g ) ⊗ L (\hat{V}_{g})^{\otimes L} as an arbitrary linear representation of the group 𝒢 \mathcal{G}
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C.-Y. Huang, X. Chen, and F.-L. Lin, pre-print arXiv:1303.4190
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Strictly speaking, for each site it would be enough to keep a one-dimensional subspace 𝕍 ~ ⊆ ( ℂ 2 ) l ⊗ ( ℂ 2 ) r \tilde{\mathbb{V}}\subseteq(\mathbb{C}_{2})_{l}\otimes(\mathbb{C}_{2})_{r} corresponding to the singlet state | ψ − ⟩ |\psi^{-}\rangle
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If the symmetry group 𝒢 \mathcal{G} only has a small number of SPT phases, one can try all possible fixed-point pairs ( u ^ sym , w ^ sym ) (\hat{u}_{\mbox{\tiny sym}},\hat{w}_{\mbox{\tiny sym}}) corresponding to these phases, for which we have described an exact expression, and restrict the numerical optimization (energy minimization) to the transitional layers
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This calculation was first presented in arXiv:quant-ph/0610099, which is the arxive version of Ref. MERA
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Andrew M. Essin, Michael Hermele, Phys. Rev. B 87, 104406 (2013)
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Andrej Mesaros, Ying Ran, Phys. Rev. B 87, 155115 (2013)
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