TY - JOUR
T1 - Supersymmetric free fermions and bosons
T2 - Locality, symmetry, and topology
AU - Gong, Zongping
AU - Jonsson, Robert H.
AU - Malz, Daniel
N1 - Funding Information:
We thank Ignacio Cirac and Krishanu Roychowdhury for helpful discussions. Z.G. is supported by the Max-Planck-Harvard Research Center for Quantum Optics (MPHQ). R.H.J. gratefully acknowledges support by the Wenner-Gren Foundations. D.M. acknowledges funding from ERC Advanced Grant No. QUENOCOBA under the EU Horizon 2020 program (Grant Agreement No. 742102).
Publisher Copyright:
© 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.
PY - 2022/2/15
Y1 - 2022/2/15
N2 - Supersymmetry (SUSY), 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 SUSY 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 tenfold 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 SUSY entanglement duality in this context. These findings are illustrated by prototypical examples. In this paper, we shed light on band topology from the perspective of SUSY.
AB - Supersymmetry (SUSY), 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 SUSY 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 tenfold 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 SUSY entanglement duality in this context. These findings are illustrated by prototypical examples. In this paper, we shed light on band topology from the perspective of SUSY.
UR - http://www.scopus.com/inward/record.url?scp=85126065208&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.105.085423
DO - 10.1103/PhysRevB.105.085423
M3 - Journal article
AN - SCOPUS:85126065208
VL - 105
JO - Physical Review B
JF - Physical Review B
SN - 2469-9950
IS - 8
M1 - 085423
ER -