Topological Order in the Projected Entangled-Pair States Formalism: Transfer Operator and Boundary Hamiltonians
Abstract
We study the structure of topological phases and their boundaries in the projected entangled-pair states (PEPS) formalism. We show how topological order in a system can be identified from the structure of the PEPS transfer operator and subsequently use these findings to analyze the structure of the boundary Hamiltonian, acting on the bond variables, which reflects the entanglement properties of the system. We find that in a topological phase, the boundary Hamiltonian consists of two parts: A universal nonlocal part which encodes the nature of the topological phase and a nonuniversal part which is local and inherits the symmetries of the topological model, which helps to infer the structure of the boundary Hamiltonian and thus possibly of the physical edge modes.
Additional Information
© 2013 American Physical Society. Received 28 October 2012; revised manuscript received 27 May 2013; published 27 August 2013. We acknowledge helpful discussions with F. Verstraete. N. S. acknowledges support by the Alexander von Humboldt Foundation, the Caltech Institute for Quantum Information and Matter (an NSF Physics Frontiers Center with the support of the Gordon and Betty Moore Foundation), and NSF Grant No. PHY-0803371. D. P. acknowledges support by the Agence Nationale de la Recherche under Grant No. ANR 2010 BLANC 0406-0 and CALMIP (Toulouse) for supercomputer resources. J. I. C. acknowledges support by the EU Project AQUTE, the DFG SFB 631 and Exzellenzcluster NIM, and Catalunya Caixa. D. P.-G. acknowledges QUEVADIS and Spanish Grants QUITEMAD and No. MTM2011-26912.Attached Files
Published - PhysRevLett.111.090501.pdf
Submitted - 1210.5601v3.pdf
Supplemental Material - README.TXT
Supplemental Material - suppmat.pdf
Files
Additional details
- Alternative title
- Topological order in PEPS: Transfer operator and boundary Hamiltonians
- Eprint ID
- 41502
- Resolver ID
- CaltechAUTHORS:20130924-112319746
- Alexander von Humboldt Foundation
- Caltech Institute for Quantum Information and Matter (IQIM)
- NSF Physics Frontiers Center
- Gordon and Betty Moore Foundation
- PHY-0803371
- NSF
- ANR 2010 BLANC 0406-0
- Agence Nationale de la Recherche
- EU Project AQUTE
- SFB 631
- Deutsche Forschungsgemeinschaft (DFG)
- Exzellenzcluster NIM
- Catalunya Caixa
- QUEVADIS
- Spanish Grant QUITEMAD
- MTM2011-26912
- Spanish Grant
- Created
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2013-09-24Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter