Bulk-edge correspondence in the trimer Su-Schrieffer-Heeger model

Abstract

A remarkable feature of the trimer Su-Schrieffer-Heeger (SSH3) model is that it supports localized edge states. Although Zak's phase remains quantized for the case of a mirror-symmetric chain, it is known that it fails to take integer values in the absence of this symmetry and thus it cannot play the role of a well-defined bulk invariant in the general case. Attempts to establish a bulk-edge correspondence have been made via Green's functions or through extensions to a synthetic dimension. Here we propose a simple alternative for SSH3, utilizing the previously introduced sublattice Zak's phase, which also remains valid in the absence of mirror symmetry and for non-commensurate chains. The defined bulk quantity takes integer values, is gauge invariant, and can be interpreted as the difference of the number of edge states between a reference and a target Hamiltonian. Our derivation further predicts the exact corrections for finite open chains, is straightforwadly generalizable, and invokes a chiral-like symmetry present in this model.

11 pages + 5 pages Appendix, 9 figures, comments welcome

References in corpus (7)

• Bulk-boundary correspondence from the inter-cellular Zak phase
• Boundary Fidelity and Entanglement in the symmetry protected topological phase of the SSH model
• Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices
• Non-Hermitian generalizations of extended Su-Schrieffer-Heeger models
• Long-range hopping and indexing assumption in one-dimensional topological insulators
• Analytical solution of open crystalline linear 1D tight-binding models
• Hidden-symmetry-protected topological phases on a one-dimensional lattice

Cited by in corpus (1)

• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices