Robustness in projected entangled pair states

J. Ignacio Cirac, Spyridon Michalakis, David Pérez-García, and Norbert Schuch
Phys. Rev. B 88, 115108 – Published 6 September 2013

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.

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  • Received 16 July 2013

DOI:https://doi.org/10.1103/PhysRevB.88.115108

©2013 American Physical Society

Authors & Affiliations

J. Ignacio Cirac1, Spyridon Michalakis2, David Pérez-García3, and Norbert Schuch4

  • 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
  • 2Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
  • 3Dpto. Análisis Matemático and IMI, Universidad Complutense de Madrid, 28040 Madrid, Spain
  • 4Institute for Quantum Information, RWTH Aachen University, D-52056 Aachen, Germany

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Issue

Vol. 88, Iss. 11 — 15 September 2013

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