Symmetry protected topological phases and generalized cohomology
Open Access
- 2 May 2019
- journal article
- research article
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2019 (5) , 7
Abstract
We discuss the classification of SPT phases in condensed matter systems. We review Kitaev’s argument that SPT phases are classified by a generalized cohomology theory, valued in the spectrum of gapped physical systems [20, 23]. We propose a concrete description of that spectrum and of the corresponding cohomology theory. We compare our proposal to pre-existing constructions in the literature.Keywords
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This publication has 34 references indexed in Scilit:
- Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved ModelPhysical Review X, 2013
- Symmetry protected topological orders and the group cohomology of their symmetry groupPhysical Review B, 2013
- Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric EffectPhysical Review X, 2013
- Symmetry protection of topological phases in one-dimensional quantum spin systemsPhysical Review B, 2012
- Two-dimensional symmetry-protected topological orders and their protected gapless edge excitationsPhysical Review B, 2011
- Complete classification of one-dimensional gapped quantum phases in interacting spin systemsPhysical Review B, 2011
- Topological phases of fermions in one dimensionPhysical Review B, 2011
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological orderPhysical Review B, 2010
- Tensor-entanglement-filtering renormalization approach and symmetry-protected topological orderPhysical Review B, 2009
- Unpaired Majorana fermions in quantum wiresPhysics-Uspekhi, 2001