Matrix Factorization Approach to Bulk-Boundary Correspondence

Alase, Abhijeet

doi:10.1007/978-3-030-31960-1_4

Cited by 1 publication

(2 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. The proof requires results from the theory of matrix Wiener-Hopf factorization 6,40 . While the following argument is not self-contained, we provide references for all the necessary auxiliary theorems.…”

Section: B Theorem 2: No Spt Phasesmentioning

confidence: 99%

“…One of the most remarkable consequences of the topological classification of free-fermion systems is the bulk-boundary correspondence 5,6 . When a gapped freefermion system is not adiabatically connected to a topologically trivial free-fermion system, the obstruction to the deformation is diagnosed by a bulk topological invariant assuming different values for the two phases.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Squaring the fermion: The threefold way and the fate of zero modes

Xu,

Flynn,

Alase

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

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 noninteracting 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.

show abstract

Section: B Theorem 2: No Spt Phasesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%