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