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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. http://resolver.caltech.edu/CaltechAUTHORS:20140402-100000848

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1310.4507arXivDiscussion Paper
http://dx.doi.org/10.1103/PhysRevB.89.075119DOIArticle
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.89.075119PublisherArticle
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:IQIM, Institute for Quantum Information and Matter
Funders:
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
Classification Code:PACS: 03.67.Mn, 03.65.Vf, 64.60.ae
Record Number:CaltechAUTHORS:20140402-100000848
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20140402-100000848
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
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:02 Apr 2014 17:38
Last Modified:02 Apr 2014 17:38

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