Abstract
Recent works have proved the existence of symmetry-protected edge states in certain one-dimensional topological band insulators and superconductors at the gap-closing points which define quantum phase transitions between two topologically nontrivial phases. We show how this picture generalizes to multiband critical models belonging to any of the chiral symmetry classes AIII, BDI, or CII of noninteracting fermions in one dimension.
Highlights
The presence of topological edge states, decoupled from the bulk, is a key characteristic of symmetry-protected topological phases of quantum many-body systems [1]
In the previous sections we showed that the boundary states in unperturbed critical 1D multiband chains are connected to a topological number ν, generalizing the ordinary winding number for gapped systems to critical systems in chiral symmetry classes AIII, BDI, and CII
Building on the work by Verresen et al [10] on critical two-band BDI models in 1D, we have carried out a study of critical multiband models in any of the 1D chiral symmetry classes AIII, BDI, and CII
Summary
The presence of topological edge states, decoupled from the bulk, is a key characteristic of symmetry-protected topological phases of quantum many-body systems [1]. The possible 1D fermionic topological phases are those of the topological band insulators and mean-field superconductors [2,3], classified by the “tenfold way” [4,5,6] For this class of models the very existence of edge states is a consequence of the topologically nontrivial phase structure of the single-particle bulk states (“bulk-boundary correspondence” [7]), with their robustness against local perturbations (or uncorrelated disorder) being ensured by the symmetries enforced on the perturbations.
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