ORCID Profile
0000-0003-0270-5592
Current Organisations
Northumbria University
,
Universiteit Gent
,
University of Cambridge
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Publisher: CRC Press
Date: 02-11-2010
DOI: 10.1201/B10273
Publisher: American Physical Society (APS)
Date: 30-11-2016
Publisher: American Physical Society (APS)
Date: 18-12-2008
Publisher: Elsevier BV
Date: 07-2023
Publisher: American Physical Society (APS)
Date: 20-01-2015
Publisher: American Physical Society (APS)
Date: 26-10-2018
Publisher: Springer Science and Business Media LLC
Date: 07-01-2021
DOI: 10.1007/S00023-020-00992-4
Abstract: One of the most striking features of gapped quantum phases that exhibit topological order is the presence of long-range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a natural framework for the parameterization of gapped ground state wavefunctions which allows one to characterize topological order in terms of the virtual symmetries of the local tensors that encode the wavefunction. In their most general form, these symmetries are represented by matrix product operators acting on the virtual level, which leads to a set of algebraic rules characterizing states with topological quantum order. This construction generalizes the concepts of $${\\mathsf {G}}$$ G - and twisted injectivity the corresponding matrix product operators encode all topological features of the theory and provide a complete picture of the ground state manifold on the torus. We show how the string-net models of Levin and Wen fit within this formalism and in doing so provide a particularly intuitive interpretation of the pentagon equation for F-symbols as the pulling of matrix product operators through the string-net tensor network. Our approach paves the way to finding novel topological phases beyond string nets and elucidates the description of topological phases in terms of entanglement Hamiltonians and edge theories.
Publisher: Springer Science and Business Media LLC
Date: 18-07-2023
Publisher: American Physical Society (APS)
Date: 22-12-2008
Publisher: American Physical Society (APS)
Date: 03-02-2017
Publisher: Elsevier BV
Date: 03-2017
Publisher: IOP Publishing
Date: 07-12-2017
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
Location: United States of America
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Frank Verstraete.