Entanglement spectrum and boundary theories with projected entangled-pair states
By J. I. Cirac, D. Poilblanc, Norbert Schuch, Frank Verstraete. 2011
219 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/94b6921087fe7cd7af90a4650017d4ea68816fd3
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In Atomic and Molecular Physics, and Optics
- Norbert Schuch
- Frank Verstraete
- I. Cirac
- David Pérez-García
- J. Haegeman
- J. Dubail
- J. I. Cirac
- Andrew J. Daley
In Condensed Matter Physics
Citations in the corpus
- Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, background): “…studies, however, it has been always found that if the state |Ψ〉 has finite correlation length, then the boundary Hamiltonian is quasi-local (Cirac et al., 2011); with a suitable treatment of sectors, this also holds for symmetry-breaking (Rispler et al., 2015, 2017) and topological…”