Robustness in projected entangled pair states
Abstract
We analyze a criterion which guarantees that the ground states of certain manybody 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.10.1007/s0022001317626 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.
 Publication:

Physical Review B
 Pub Date:
 September 2013
 DOI:
 10.1103/PhysRevB.88.115108
 arXiv:
 arXiv:1306.4003
 Bibcode:
 2013PhRvB..88k5108C
 Keywords:

 71.10.w;
 03.65.Vf;
 05.30.d;
 75.10.b;
 Theories and models of manyelectron systems;
 Phases: geometric;
 dynamic or topological;
 Quantum statistical mechanics;
 General theory and models of magnetic ordering;
 Condensed Matter  Strongly Correlated Electrons;
 Quantum Physics
 EPrint:
 11 pages, 4 figures