Document Zbl 1436.81160

The bulk-edge correspondence in three simple cases. (English) Zbl 1436.81160

Rev. Math. Phys. 32, No. 3, Article ID 2030003, 37 p. (2020).

Summary: We present examples in three symmetry classes of topological insulators in one or two dimensions where the proof of the bulk-edge correspondence is particularly simple. This serves to illustrate the mechanism behind the bulk-edge principle without the overhead of the more general proofs which are available. We also give a new formula for the \(\mathbb{Z}_2\)-index of our time-reversal invariant systems inspired by J. E. Moore and L. Balents [“Topological invariants of time-reversal-invariant band structures”, Phys. Rev. B 75, No. 12, Article ID 121306, 4 p. (2007; doi:10.1103/PhysRevB.75.121306)].

Cited in 6 Documents

MSC:

81V70	Many-body theory; quantum Hall effect
14D21	Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
35Q40	PDEs in connection with quantum mechanics
46N50	Applications of functional analysis in quantum physics
47N50	Applications of operator theory in the physical sciences
58D30	Applications of manifolds of mappings to the sciences

Keywords:

topological insulators; translation invariance; time-reversal invariance

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References:

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