Perturbative 2-body Parent Hamiltonians for Projected Entangled Pair States

We construct parent Hamiltonians involving only local 2-body interactions for a broad class of Projected Entangled Pair States (PEPS). Making use of perturbation gadget techniques, we define a perturbative Hamiltonian acting on the virtual PEPS space with a finite order low energy effective Hamilton...

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Bibliographic Details
Published in:arXiv.org 2014-12
Main Authors: Brell, Courtney G, Bartlett, Stephen D, Doherty, Andrew C
Format: Article
Language:English
Subjects:
Coding
Concrete construction
Perturbation theory
Online Access:Get full text
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Summary:We construct parent Hamiltonians involving only local 2-body interactions for a broad class of Projected Entangled Pair States (PEPS). Making use of perturbation gadget techniques, we define a perturbative Hamiltonian acting on the virtual PEPS space with a finite order low energy effective Hamiltonian that is a gapped, frustration-free parent Hamiltonian for an encoded version of a desired PEPS. For topologically ordered PEPS, the ground space of the low energy effective Hamiltonian is shown to be in the same phase as the desired state to all orders of perturbation theory. An encoded parent Hamiltonian for the double semion string net ground state is explicitly constructed as a concrete example.
ISSN:2331-8422
DOI:10.48550/arxiv.1407.4829