Twisted injectivity in projected entangled pair states and the classification of quantum phases |
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Authors: | Oliver Buerschaper |
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Institution: | Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada, N2L 2Y5 |
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Abstract: | We introduce a class of projected entangled pair states (PEPS) which is based on a group symmetry twisted by a 3-cocycle of the group. This twisted symmetry is expressed as a matrix product operator (MPO) with bond dimension greater than 1 and acts on the virtual boundary of a PEPS tensor. We show that it gives rise to a new standard form for PEPS from which we construct a family of local Hamiltonians which are gapped, frustration-free and include fixed points of the renormalization group flow. Based on this insight, we advance the classification of 2D gapped quantum spin systems by showing how this new standard form for PEPS determines the emergent topological order of these local Hamiltonians. Specifically, we identify their universality class as Dijkgraaf–Witten topological quantum field theory (TQFT). |
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Keywords: | Classification of quantum phases Topological order Projected entangled pair states Matrix product operators Group cohomology Tensor networks |
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