For spectrally gapped, time-reversal-invariant, exponentially local 2D Hamiltonians, the Z2 bulk index equals the mod-2 index of an edge Fredholm operator.
Local formula for the $Z_2$ invariant of topological insulators
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abstract
We proposed a formula for the $Z_2$ invariant for topological insulators, which remains valid without translational invariance. Our formula is a local expression, in the sense that the contributions mainly come from quantities near a point. Using almost commute matrices, we proposed a method to approximate this invariant with local information. The validity of the formula and the approximation method is proved.
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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.