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Entanglement compression in scale space : from the multiscale entanglement renormalization ansatz to matrix product operators

Karel Van Acoleyen (UGent) , Andrew Hallam (UGent) , Matthias Bal (UGent) , Markus Hauru (UGent) , Jutho Haegeman (UGent) and Frank Verstraete (UGent)
(2020) PHYSICAL REVIEW B. 102(16).
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Abstract
The multiscale entanglement renormalization ansatz (MERA) provides a constructive algorithm for realizing wave functions that are inherently scale invariant. Unlike conformally invariant partition functions, however, the finite bond dimension chi of the MERA provides a cutoff in the fields that can be realized. In this paper, we demonstrate that this cutoff is equivalent to the one obtained when approximating a thermal state of a critical Hamiltonian with a matrix product operator (MPO) of finite bond dimension chi. This is achieved by constructing an explicit mapping between the isometrics of the MERA and the local tensors of the MPO. In terms of energy scales, our results show that a finite bond dimension MERA is equivalent to introducing both an infrared and an ultraviolet scale, characterizing relevant and irrelevant perturbations on the underlying conformal field theory.
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UNIVERSALITY

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MLA
Van Acoleyen, Karel, et al. “Entanglement Compression in Scale Space : From the Multiscale Entanglement Renormalization Ansatz to Matrix Product Operators.” PHYSICAL REVIEW B, vol. 102, no. 16, 2020, doi:10.1103/physrevb.102.165131.
APA
Van Acoleyen, K., Hallam, A., Bal, M., Hauru, M., Haegeman, J., & Verstraete, F. (2020). Entanglement compression in scale space : from the multiscale entanglement renormalization ansatz to matrix product operators. PHYSICAL REVIEW B, 102(16). https://doi.org/10.1103/physrevb.102.165131
Chicago author-date
Van Acoleyen, Karel, Andrew Hallam, Matthias Bal, Markus Hauru, Jutho Haegeman, and Frank Verstraete. 2020. “Entanglement Compression in Scale Space : From the Multiscale Entanglement Renormalization Ansatz to Matrix Product Operators.” PHYSICAL REVIEW B 102 (16). https://doi.org/10.1103/physrevb.102.165131.
Chicago author-date (all authors)
Van Acoleyen, Karel, Andrew Hallam, Matthias Bal, Markus Hauru, Jutho Haegeman, and Frank Verstraete. 2020. “Entanglement Compression in Scale Space : From the Multiscale Entanglement Renormalization Ansatz to Matrix Product Operators.” PHYSICAL REVIEW B 102 (16). doi:10.1103/physrevb.102.165131.
Vancouver
1.
Van Acoleyen K, Hallam A, Bal M, Hauru M, Haegeman J, Verstraete F. Entanglement compression in scale space : from the multiscale entanglement renormalization ansatz to matrix product operators. PHYSICAL REVIEW B. 2020;102(16).
IEEE
[1]
K. Van Acoleyen, A. Hallam, M. Bal, M. Hauru, J. Haegeman, and F. Verstraete, “Entanglement compression in scale space : from the multiscale entanglement renormalization ansatz to matrix product operators,” PHYSICAL REVIEW B, vol. 102, no. 16, 2020.
@article{8714411,
  abstract     = {{The multiscale entanglement renormalization ansatz (MERA) provides a constructive algorithm for realizing wave functions that are inherently scale invariant. Unlike conformally invariant partition functions, however, the finite bond dimension chi of the MERA provides a cutoff in the fields that can be realized. In this paper, we demonstrate that this cutoff is equivalent to the one obtained when approximating a thermal state of a critical Hamiltonian with a matrix product operator (MPO) of finite bond dimension chi. This is achieved by constructing an explicit mapping between the isometrics of the MERA and the local tensors of the MPO. In terms of energy scales, our results show that a finite bond dimension MERA is equivalent to introducing both an infrared and an ultraviolet scale, characterizing relevant and irrelevant perturbations on the underlying conformal field theory.}},
  articleno    = {{165131}},
  author       = {{Van Acoleyen, Karel and Hallam, Andrew and Bal, Matthias and Hauru, Markus and Haegeman, Jutho and Verstraete, Frank}},
  issn         = {{2469-9950}},
  journal      = {{PHYSICAL REVIEW B}},
  keywords     = {{UNIVERSALITY}},
  language     = {{eng}},
  number       = {{16}},
  pages        = {{5}},
  title        = {{Entanglement compression in scale space : from the multiscale entanglement renormalization ansatz to matrix product operators}},
  url          = {{http://doi.org/10.1103/physrevb.102.165131}},
  volume       = {{102}},
  year         = {{2020}},
}
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