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.

arXiv comment12 pages, 6 figures

References in corpus (43)

• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Higher-Order Topological Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topolectrical circuit realization of topological corner modes
• Topolectrical circuits
• The Zak phase and the existence of edge states in graphene
• Novel Topological Phase with Zero Berry Curvature
• Experimental realization and characterization of an electronic Lieb lattice
• Topological states in engineered atomic lattices
• Nonlinear conduction via solitons in a topological mechanical insulator
• Topological phases of generalized Su-Schrieffer-Heeger models
• Chiral Ladders and the Edges of Chern Insulators
• Topological characterization of chiral models through their long time dynamics
• Dimensional Crossover of Topological Edge States in Su-Schrieffer-Heeger Model
• Topological characterizations of an extended Su-Schrieffer-Heeger model
• Interplay between long range hopping and disorder in topological systems
• Topological edge states of interacting photon pairs emulated in a topolectrical circuit
• Topological tight-binding models from non-trivial square roots
• Real-space imaging of a topological protected edge state with ultracold atoms in an amplitude-chirped optical lattice
• Observation of edge waves in a two-dimensional Su-Schrieffer-Heeger acoustic network
• A two-leg Su-Schrieffer-Heeger chain with glide reflection symmetry
• Probing one-dimensional topological phases in waveguide lattices with broken chiral symmetry
• An elementary rigorous proof of bulk-boundary correspondence in the generalized Su-Schrieffer-Heeger model
• One-dimensional $2^n$-root topological insulators and superconductors
• Topological edge states with ultracold atoms carrying orbital angular momentum in a diamond chain
• Topological Anderson insulating phases in the long-range Su-Schrieffer-Heeger model
• One-dimensional topological insulators with noncentered inversion symmetry axis
• Second-order topological corner states with ultracold atoms carrying orbital angular momentum in optical lattices
• $2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals
• Topological edge states and Aharanov-Bohm caging with ultracold atoms carrying orbital angular momentum
• Diagonalization of quasi-uniform tridiagonal matrices
• Topological and non-topological features of generalized Su-Schrieffer-Heeger models
• Matryoshka approach to Sine-Cosine topological models
• Exact edge, bulk and bound states of finite topological systems
• Analytical solution of open crystalline linear 1D tight-binding models
• Hidden-symmetry-protected topological phases on a one-dimensional lattice
• Theory of edge states based on the hermiticity of tight-binding Hamiltonian operators
• Symmetry protected weak topological phases in a superlattice
• Calculating the polarization in bi-partite lattice models: application to an extended Su-Schrieffer-Heeger model
• Hidden-symmetry-protected quantum pseudo-spin Hall effect in optical lattices
• 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