Jeongwan Haah

Bifurcation in entanglement renormalization group flow of a gapped spin model

We study entanglement renormalization group transformations for the ground states of a spin model H_A, called cubic code model in three dimensions, in order to understand long-range entanglement structure. The cubic code model has degenerate and locally indistinguishable ground states under periodic boundary conditions. So this model may be regarded as topologically ordered. In the entanglement renormalization, one applies local unitary transformations on a state, called disentangling transformations, after which some of the spins are completely disentangled from the rest and then discarded. We find a disentangling unitary to establish equivalence of the ground state of H_A on a lattice of lattice spacing a to the tensor product of ground spaces of two independent Hamiltonians H_A and H_B on lattices of lattice spacing 2a. We further find a disentangling unitary for the ground space of H_B with the lattice spacing a to show that it decomposes into two copies of itself on the lattice of the lattice spacing 2a. The disentangling transformations yield a tensor network description, a branching MERA, for the ground state of the original model.

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