The classification of symmetry protected topological phases of one-dimensional fermion systems

• URL: http://arxiv.org/abs/2006.15232v2
• Date: Wed, 17 Feb 2021 07:08:56 GMT
• Title: The classification of symmetry protected topological phases of one-dimensional fermion systems
• Authors: Chris Bourne and Yoshiko Ogata
• Abstract summary: We introduce an index for symmetry protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group $G$. This index takes values in $mathbbZ times H1(G,mathbbZ_2) times H2(G, U(1)_mathfrakp)$ with a generalized Wall group law under stacking.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce an index for symmetry protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group $G$. This index takes values in $\mathbb{Z}_2 \times H^1(G,\mathbb{Z}_2) \times H^2(G, U(1)_{\mathfrak{p}})$ with a generalized Wall group law under stacking. We show that this index is an invariant of the classification of SPT phases. When the ground state is translation invariant and has reduced density matrices with uniformly bounded rank on finite intervals, we derive a fermionic matrix product representative of this state with on-site symmetry.

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