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Published September 6, 2013 | Submitted + Published
Journal Article Open

Robustness in projected entangled pair states

Abstract

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.

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.

Attached Files

Published - PhysRevB.88.115108.pdf

Submitted - 1306.4003v1.pdf

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