For spectrally gapped, time-reversal-invariant, exponentially local 2D Hamiltonians, the Z2 bulk index equals the mod-2 index of an edge Fredholm operator.
The bulk-edge correspondence for continuous honeycomb lattices
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abstract
We study bulk/edge aspects of continuous honeycomb lattices in a magnetic field. We compute the bulk index of Bloch eigenbundles: it equals $2$ or $-2$, with sign depending on nearby Dirac points and on the magnetic field. We then prove the existence of two topologically protected waves propagating along line defects. This shows the bulk/edge correspondence for our class of Hamiltonians.
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math-ph 1years
2019 1verdicts
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Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory
For spectrally gapped, time-reversal-invariant, exponentially local 2D Hamiltonians, the Z2 bulk index equals the mod-2 index of an edge Fredholm operator.