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Matrix product operators for symmetry-protected topological phases: Gauging and edge theories

Autor(en)
Dominic J. Williamson, Nick Bultinck, Michael Marien, Mehmet B. Sahinoglu, Jutho Haegeman, Frank Verstraete
Abstrakt

Projected entangled pair states (PEPS) provide a natural ansatz for the ground states of gapped, local Hamiltonians in which global characteristics of a quantum state are encoded in properties of local tensors. We develop a framework to describe onsite symmetries, as occurring in systems exhibiting symmetry-protected topological (SPT) quantum order, in terms of virtual symmetries of the local tensors expressed as a set of matrix product operators (MPOs) labeled by distinct group elements. These MPOs describe the possibly anomalous symmetry of the edge theory, whose local degrees of freedom are concretely identified in a PEPS. A classification of SPT phases is obtained by studying the obstructions to continuously deforming one set of MPOs into another, recovering the results derived for fixed-point models [Chen et al., Phys. Rev. B 87, 155114 (2013)]. Our formalism accommodates perturbations away from fixed-point models, opening the possibility of studying phase transitions between different SPT phases. We also demonstrate that applying the recently developed quantum state gauging procedure to a SPT PEPS yields a PEPS with topological order determined by the initial symmetry MPOs. The MPO framework thus unifies the different approaches to classifying SPT phases, via fixed-point models, boundary anomalies, or gauging the symmetry, into the single problem of classifying inequivalent sets of matrix product operator symmetries that are defined purely in terms of a PEPS.

Organisation(en)
Quantenoptik, Quantennanophysik und Quanteninformation
Externe Organisation(en)
Ghent University
Journal
Physical Review B
Band
94
Anzahl der Seiten
32
ISSN
1098-0121
DOI
https://doi.org/10.1103/PhysRevB.94.205150
Publikationsdatum
11-2016
Peer-reviewed
Ja
ÖFOS 2012
103025 Quantenmechanik, 103015 Kondensierte Materie
Schlagwörter
ASJC Scopus Sachgebiete
Electronic, Optical and Magnetic Materials, Condensed Matter Physics
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/ff5bbd62-ffc2-4a70-8e1c-3ffb8f21800d