Bifurcation in entanglement renormalization group flow of a gapped spin model
- Creators
- Haah, Jeongwan
Abstract
We study entanglement renormalization group transformations for the ground states of a spin model, called cubic code model H_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_A on a lattice of lattice spacing ɑ to the tensor product of ground spaces of two independent Hamiltonians H_A and H_B on lattices of lattice spacing 2ɑ. 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 2ɑ. 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_A and H_B represent distinct phases of matter.
Additional Information
© 2014 American Physical Society. Received 22 October 2013; published 18 February 2014. The author would like to thank G. Vidal for raising a question that has resulted in this work. The author also thanks J. Preskill and G. Evenbly for numerous helpful discussions. A part of this work was done at IBM Watson Research Center, Yorktown Heights, New York. The author is supported in part by Caltech Institute for Quantum Information and Matter, a NSF Physics Frontier Center with support from Gordon and Betty Moore Foundation, and by MIT Pappalardo Fellowship in Physics.Attached Files
Published - PhysRevB.89.075119.pdf
Submitted - 1310.4507v2.pdf
Supplemental Material - codeRG2-output.pdf
Supplemental Material - codeRG2.nb
Files
Additional details
- Eprint ID
- 44603
- Resolver ID
- CaltechAUTHORS:20140402-100000848
- Institute for Quantum Information and Matter (IQIM)
- NSF Physics Frontier Center
- Gordon and Betty Moore Foundation
- MIT Pappalardo Fellowship in Physics
- Created
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2014-04-02Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter