Bifurcation in entanglement renormalization group flow of a gapped spin model
Name
Haah-2014-Bifurcation in entanglement.pdf
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281.83 KB
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Author(s)
Haah, Jeongwan
Date Issued
February 2014
Journal
Physical Review B
Publisher
American Physical Society
Citation
Haah, Jeongwan. “Bifurcation in Entanglement Renormalization Group Flow of a Gapped Spin Model.” Phys. Rev. B 89, no. 7 (February 2014). © 2014 American Physical Society
Version
Final published version
Abstract
We study entanglement renormalization group transformations for the ground states of a spin model, called cubic code model H[subscript A] 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. 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[subscript A] on a lattice of lattice spacing a to the tensor product of ground spaces of two independent Hamiltonians H[subscript A] and H[subscript B] on lattices of lattice spacing 2a. We further find a disentangling unitary for the ground space of H[subscript 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 for the ground state of the cubic code model. Using exact formulas for the degeneracy as a function of system size, we show that the two Hamiltonians H[subscript A] and H[subscript B] represent distinct phases of matter.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.89.075119
