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Entanglement spectrum and boundary theories with projected entangled-pair states

J Ignacio Cirac, Didier Poilblanc, Norbert Schuch and Frank Verstraete (UGent)
(2011) PHYSICAL REVIEW B. 83(24).
Author
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Abstract
In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated with their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using projected entangled-pair states. This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models: a deformed AKLT model [I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987)], an Ising-type model [F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006)], and Kitaev's toric code [A. Kitaev, Ann. Phys. 303, 2 (2003)], both in finite ladders and in infinite square lattices. In the second case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield nonlocal Hamiltonians. Because our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary.
Keywords
BOND GROUND-STATES, RENORMALIZATION-GROUP, QUANTUM, ANTIFERROMAGNETS

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MLA
Cirac, J. Ignacio, et al. “Entanglement Spectrum and Boundary Theories with Projected Entangled-Pair States.” PHYSICAL REVIEW B, vol. 83, no. 24, 2011, doi:10.1103/PhysRevB.83.245134.
APA
Cirac, J. I., Poilblanc, D., Schuch, N., & Verstraete, F. (2011). Entanglement spectrum and boundary theories with projected entangled-pair states. PHYSICAL REVIEW B, 83(24). https://doi.org/10.1103/PhysRevB.83.245134
Chicago author-date
Cirac, J Ignacio, Didier Poilblanc, Norbert Schuch, and Frank Verstraete. 2011. “Entanglement Spectrum and Boundary Theories with Projected Entangled-Pair States.” PHYSICAL REVIEW B 83 (24). https://doi.org/10.1103/PhysRevB.83.245134.
Chicago author-date (all authors)
Cirac, J Ignacio, Didier Poilblanc, Norbert Schuch, and Frank Verstraete. 2011. “Entanglement Spectrum and Boundary Theories with Projected Entangled-Pair States.” PHYSICAL REVIEW B 83 (24). doi:10.1103/PhysRevB.83.245134.
Vancouver
1.
Cirac JI, Poilblanc D, Schuch N, Verstraete F. Entanglement spectrum and boundary theories with projected entangled-pair states. PHYSICAL REVIEW B. 2011;83(24).
IEEE
[1]
J. I. Cirac, D. Poilblanc, N. Schuch, and F. Verstraete, “Entanglement spectrum and boundary theories with projected entangled-pair states,” PHYSICAL REVIEW B, vol. 83, no. 24, 2011.
@article{8589154,
  abstract     = {{In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated with their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using projected entangled-pair states. This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models: a deformed AKLT model [I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987)], an Ising-type model [F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006)], and Kitaev's toric code [A. Kitaev, Ann. Phys. 303, 2 (2003)], both in finite ladders and in infinite square lattices. In the second case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield nonlocal Hamiltonians. Because our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary.}},
  articleno    = {{245134}},
  author       = {{Cirac, J Ignacio and Poilblanc, Didier and Schuch, Norbert and Verstraete, Frank}},
  issn         = {{1098-0121}},
  journal      = {{PHYSICAL REVIEW B}},
  keywords     = {{BOND GROUND-STATES,RENORMALIZATION-GROUP,QUANTUM,ANTIFERROMAGNETS}},
  language     = {{eng}},
  number       = {{24}},
  pages        = {{12}},
  title        = {{Entanglement spectrum and boundary theories with projected entangled-pair states}},
  url          = {{http://doi.org/10.1103/PhysRevB.83.245134}},
  volume       = {{83}},
  year         = {{2011}},
}
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