Long-range hopping and indexing assumption in one-dimensional topological insulators

Abstract

In this paper, we show that the introduction of long-range hoppings in 1D topological insulator models implies that different possibilities of site indexing must be considered when determining the bulk topological invariants in order to avoid the existence of hidden symmetries. The particular case of the extended SSH chain is addressed as an example where such behavior occurs. In this model, the introduction of long-range hopping terms breaks the bipartite property and a band inversion occurs in the band structure as the relative values of the hopping terms change, signaling a crossover between hopping parameter regions of "influence" of different chiral symmetries. Furthermore, edge states become a linear combination of edge-like states with different localization lengths and reflect the gradual transition between these different chiral symmetries.

12 pages, 6 figures

References in corpus (14)

• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Novel Topological Phase with Zero Berry Curvature
• Nonlinear conduction via solitons in a topological mechanical insulator
• Topological characterizations of an extended Su-Schrieffer-Heeger model
• One-dimensional $2^n$-root topological insulators and superconductors
• One-dimensional topological insulators with noncentered inversion symmetry axis
• $2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals
• Second-order topological corner states with ultracold atoms carrying orbital angular momentum in optical lattices
• Matryoshka approach to Sine-Cosine topological models
• Analytical solution of open crystalline linear 1D tight-binding models
• Hidden-symmetry-protected topological phases on a one-dimensional lattice
• Calculating the polarization in bi-partite lattice models: application to an extended Su-Schrieffer-Heeger model
• Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice
• Effects of correlations on phase diagrams of the two-dimensional Su-Schrieffer-Heeger model with the longer-range hoppings

Cited by in corpus (14)

• Bulk-edge correspondence in the trimer Su-Schrieffer-Heeger model
• Bulk-boundary correspondence in extended trimer Su-Schrieffer-Heeger model
• Competition of long-range interactions and noise at ramped quench dynamical quantum phase transition: The case of the long-range pairing Kitaev chain
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
• Subradiant edge states in an atom chain with waveguide-mediated hopping
• Topological Phases of Tight-Binding Trimer Lattice in the BDI Symmetry Class
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Multiple polaritonic edge states in a Su-Schrieffer-Heeger chain strongly coupled to a multimode cavity
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Interaction-induced phase transitions at topological quantum criticality of an extended Su-Schrieffer-Heeger model
• Topological photon pumping in quantum optical systems
• A new class of higher-order topological insulators that localize energy at arbitrary multiple sites
• Multipartite entanglement distribution in a topological photonic network
• Emergent topological phases in an extended Su-Schrieffer-Heeger model with Rashba spin-orbit interaction, higher order hopping and domain wall