Supersymmetric Free Fermions and Bosons: Locality, Symmetry and Topology
- URL: http://arxiv.org/abs/2112.07527v3
- Date: Mon, 14 Mar 2022 10:39:45 GMT
- Title: Supersymmetric Free Fermions and Bosons: Locality, Symmetry and Topology
- Authors: Zongping Gong, Robert H. Jonsson, Daniel Malz
- Abstract summary: Supersymmetry refers to a dual relation that connects fermionic and bosonic degrees of freedom in a system.
Recently, there has been considerable interest in applying the idea of supersymmetry to topological phases, motivated by the attempt to gain insights from the fermion side into the boson side and vice versa.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Supersymmetry, originally proposed in particle physics, refers to a dual
relation that connects fermionic and bosonic degrees of freedom in a system.
Recently, there has been considerable interest in applying the idea of
supersymmetry to topological phases, motivated by the attempt to gain insights
from the fermion side into the boson side and vice versa. We present a
systematic study of this construction when applied to band topology in
noninteracting systems. First, on top of the conventional ten-fold way, we find
that topological insulators and superconductors are divided into three classes
depending on whether the supercharge can be local and symmetric, must break a
symmetry to preserve locality, or needs to break locality. Second, we resolve
the apparent paradox between the nontriviality of free fermions and the
triviality of free bosons by noting that the topological information is encoded
in the identification map. We also discuss how to understand a recently
revealed supersymmetric entanglement duality in this context. These findings
are illustrated by prototypical examples. Our work sheds new light on band
topology from the perspective of supersymmetry.
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