Squaring the fermion: The threefold way and the fate of zero modes
- URL: http://arxiv.org/abs/2005.05986v2
- Date: Thu, 25 Jun 2020 03:24:43 GMT
- Title: Squaring the fermion: The threefold way and the fate of zero modes
- Authors: Qiao-Ru Xu, Vincent P. Flynn, Abhijeet Alase, Emilio Cobanera, Lorenza
Viola, and Gerardo Ortiz
- Abstract summary: We investigate topological properties and classification of mean-field theories of stable bosonic systems.
Of the three standard classifying symmetries, only time-reversal represents a real symmetry of the many-boson system.
We unveil an elegant threefold-way topological classification of non-interacting bosons.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We investigate topological properties and classification of mean-field
theories of stable bosonic systems. Of the three standard classifying
symmetries, only time-reversal represents a real symmetry of the many-boson
system, while the other two, particle-hole and chiral, are simply constraints
that manifest as symmetries of the effective single-particle problem. For
gapped systems in arbitrary space dimension we establish three fundamental
no-go theorems that prove the absence of: parity switches,
symmetry-protected-topological quantum phases, and localized bosonic zero modes
under open boundary conditions. We then introduce a squaring, kernel-preserving
map connecting non-interacting Hermitian theories of fermions and stable boson
systems, which serves as a playground to reveal the role of topology in bosonic
phases and their localized midgap boundary modes. Finally, we determine the
symmetry classes inherited from the fermionic tenfold-way classification,
unveiling an elegant threefold-way topological classification of
non-interacting bosons. We illustrate our main findings in one- and
two-dimensional bosonic lattice and field-theory models.
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