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Fermionic projected entangled-pair states and topological phases

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QUTE (Quantum Tensor Networks and Entanglement)
Abstract
We study fermionic matrix product operator algebras and identify the associated algebraic data. Using this algebraic data we construct fermionic tensor network states in two dimensions that have non-trivial symmetry-protected or intrinsic topological order. The tensor network states allow us to relate physical properties of the topological phases to the underlying algebraic data. We illustrate this by calculating defect properties and modular matrices of supercohomology phases. Our formalism also captures Majorana defects as we show explicitly for a class of $\mathbb{Z}_2$ symmetry-protected and intrinsic topological phases. The tensor networks states presented here are well-suited for numerical applications and hence open up new possibilities for studying interacting fermionic topological phases.
Keywords
tensor networks, topological phases, strongly correlated electrons

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Citation

Please use this url to cite or link to this publication:

Chicago
Bultinck, Nick, Dominic J Williamson, Jutho Haegeman, and Frank Verstraete. 2018. “Fermionic Projected Entangled-pair States and Topological Phases.” Journal of Physics A-mathematical and Theoretical 51 (2).
APA
Bultinck, N., Williamson, D. J., Haegeman, J., & Verstraete, F. (2018). Fermionic projected entangled-pair states and topological phases. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 51(2).
Vancouver
1.
Bultinck N, Williamson DJ, Haegeman J, Verstraete F. Fermionic projected entangled-pair states and topological phases. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2018;51(2).
MLA
Bultinck, Nick, Dominic J Williamson, Jutho Haegeman, et al. “Fermionic Projected Entangled-pair States and Topological Phases.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 51.2 (2018): n. pag. Print.
@article{8556824,
  abstract     = {We study fermionic matrix product operator algebras and identify the associated algebraic data. Using this algebraic data we construct fermionic tensor network states in two dimensions that have non-trivial symmetry-protected or intrinsic topological order. The tensor network states allow us to relate physical properties of the topological phases to the underlying algebraic data. We illustrate this by calculating defect properties and modular matrices of supercohomology phases. Our formalism also captures Majorana defects as we show explicitly for a class of \${\textbackslash}mathbb\{Z\}\_2\$  symmetry-protected and intrinsic topological phases. The tensor networks states presented here are well-suited for numerical applications and hence open up new possibilities for studying interacting fermionic topological phases.},
  articleno    = {025202},
  author       = {Bultinck, Nick and Williamson, Dominic J and Haegeman, Jutho and Verstraete, Frank},
  issn         = {1751-8113},
  journal      = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
  keyword      = {tensor networks,topological phases,strongly correlated electrons},
  language     = {eng},
  number       = {2},
  pages        = {41},
  title        = {Fermionic projected entangled-pair states and topological phases},
  url          = {http://dx.doi.org/10.1088/1751-8121/aa99cc},
  volume       = {51},
  year         = {2018},
}

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