Entanglement spectrum and boundary theories with projected entangled-pair states

Autor(en)

J. Ignacio Cirac, Didier Poilblanc, Norbert Schuch, Frank Verstraete

Abstrakt

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.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Max-Planck-Institut für Quantenoptik, Centre National De La Recherche Scientifique (CNRS), California Institute of Technology (Caltech)

Journal

Physical Review B

Band

83

Anzahl der Seiten

12

ISSN

1098-0121

DOI

https://doi.org/10.1103/PhysRevB.83.245134

Publikationsdatum

06-2011

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik

Schlagwörter

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/cfb76033-aa27-4b32-99d6-8b2ed90e1751