A Caltech Library Service

Robustness in projected entangled pair states

Cirac, J. Ignacio and Michalakis, Spyridon and Pérez-García, David and Schuch, Norbert (2013) Robustness in projected entangled pair states. Physical Review B, 88 (11). Art. No. 115108. ISSN 1098-0121. doi:10.1103/PhysRevB.88.115108.

PDF - Published Version
See Usage Policy.

PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


We analyze a criterion which guarantees that the ground states of certain many-body systems are stable under perturbations. Specifically, we consider PEPS, which are believed to provide an efficient description, based on local tensors, for the low energy physics arising from local interactions. In order to assess stability in the framework of PEPS, one thus needs to understand how physically allowed perturbations of the local tensor affect the properties of the global state. In this paper, we show that a restricted version of the local topological quantum order (LTQO) condition [Michalakis and Pytel, Commun. Math. Phys. 322, 277 (2013)] provides a checkable criterion which allows us to assess the stability of local properties of PEPS under physical perturbations. We moreover show that LTQO itself is stable under perturbations which preserve the spectral gap, leading to nontrivial examples of PEPS which possess LTQO and are thus stable under arbitrary perturbations.

Item Type:Article
Related URLs:
URLURL TypeDescription DOIArticle Paper
Cirac, J. Ignacio0000-0003-3359-1743
Michalakis, Spyridon0000-0003-4963-1156
Pérez-García, David0000-0003-2990-791X
Additional Information:© 2013 American Physical Society. Received 16 July 2013; published 6 September 2013. We are indebted to Frank Verstraete for many useful comments on this work. J.I.C. acknowledges support by the EU project AQUTE, the DFG SFB 631 and Exzellenzcluster NIM, and Catalunya Caixa. S.M. acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant No. GBMF1250 and by the AFOSR Grant No. FA8750-12-2-0308. D.P.G. acknowledges support from Spanish Grant Nos. MTM2011- 26912 and QUITEMAD, and European CHIST-ERA project CQC. N.S. acknowledges support by the Alexander von Humboldt foundation.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)SFB 631
Exzellenzcluster NIMUNSPECIFIED
Catalunya CaixaUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
Air Force Office of Scientific Research (AFOSR)FA8750-12-2-0308
Spanish GrantMTM2011-26912
Alexander von Humboldt FoundationUNSPECIFIED
Issue or Number:11
Classification Code:PACS: 71.10.-w, 03.65.Vf, 05.30.-d, 75.10.-b
Record Number:CaltechAUTHORS:20131004-092235258
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41676
Deposited By: Tony Diaz
Deposited On:04 Oct 2013 17:25
Last Modified:10 Nov 2021 04:33

Repository Staff Only: item control page