Supersymmetric Free Fermions and Bosons: Locality, Symmetry and Topology
arXiv:2112.07527 · doi:10.1103/PhysRevB.105.085423
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.
arXiv comment12 pages, 3 figures, 1 table, (close to) published version
References in corpus (27)
- Topological Insulators
- Topological insulators and superconductors
- Unpaired Majorana fermions in quantum wires
- Classification of topological insulators and superconductors in three spatial dimensions
- Classification of topological quantum matter with symmetries
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Periodic table for topological insulators and superconductors
- Exceptional Topology of Non-Hermitian Systems
- Non-Hermitian Physics
- Topological phases of non-Hermitian systems
- Topological phases of fermions in one dimension
- Topological Defects and Gapless Modes in Insulators and Superconductors
- Topological chiral magnonic edge mode in a magnonic crystal
- Exponential localization of Wannier functions in insulators
- Entanglement spectrum of topological insulators and superconductors
- Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
- Compactly-supported Wannier functions and algebraic -theory
- Topology by Dissipation: Majorana Bosons in Metastable Quadratic Markovian Dynamics
- Symmetries and boundary theories for chiral Projected Entangled Pair States
- Squaring the fermion: The threefold way and the fate of zero modes
- Supersymmetry in the nonsupersymmetric Sachdev-Ye-Kitaev model
- Topological Mechanics from Supersymmetry
- Minimal energy cost of entanglement extraction
- A classification of magnetic frustration and metamaterials from topology
- Entanglement dualities in supersymmetry
- Vanishing Hall conductance for commuting Hamiltonians