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Bifurcation in entanglement renormalization group flow of a gapped spin model

Haah, Jeongwan (2014) Bifurcation in entanglement renormalization group flow of a gapped spin model. Physical Review B, 89 (7). Art. No. 075119. ISSN 1098-0121. doi:10.1103/PhysRevB.89.075119.

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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.

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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.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontier CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
MIT Pappalardo Fellowship in PhysicsUNSPECIFIED
Issue or Number:7
Classification Code:PACS: 03.67.Mn, 03.65.Vf,
Record Number:CaltechAUTHORS:20140402-100000848
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Official Citation: Bifurcation in entanglement renormalization group flow of a gapped spin model Jeongwan Haah Phys. Rev. B 89, 075119 (2014) – Published 18 February 2014
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:44603
Deposited By: Ruth Sustaita
Deposited On:02 Apr 2014 17:38
Last Modified:10 Nov 2021 16:54

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