Speaker
Description
Recent advances in topological condensed matter physics have highlighted the importance of simple one-dimensional lattice models as building blocks for understanding more complex quantum systems. In particular, the Su–Schrieffer–Heeger (SSH) model has become a paradigmatic example of how topology controls the existence and robustness of eigenstates in low-dimensional systems. However, when the SSH model is generalized to include longer-range hopping beyond nearest neighbours, the structure and number of eigenstates is no longer trivial and remains only partially understood.
A key open question is how the number and nature of eigenstates depend on the coupling parameters when additional links between non-nearest-neighbour sites are introduced, especially in the infinite-chain limit.
In this work, we study a family of generalized SSH models (SSH-N chains) that include hoppings beyond nearest neighbours. Using a combination of analytical methods and numerical simulations, we solve the resulting lattice Hamiltonians by applying Bloch’s theorem and constructing the corresponding band structure and eigenmodes.
We find that the number and type of eigenstates depend sensitively on the geometry of the unit cell and on the values of the coupling parameters. In contrast to the standard SSH model, which supports only a fixed number of edge and bulk states, extended hopping gives rise to new families of solutions, including exponentially localized wave functions in finite systems and additional allowed linear combinations in the bulk.
These results clarify how long-range couplings modify the spectral and topological structure of SSH-type models and provide a systematic framework for engineering new quantum states in one-dimensional lattices, with potential applications to photonic, cold-atom, and molecular lattice systems.
| Keyword-1 | SSH model |
|---|---|
| Keyword-2 | Condensed matter theory |
| Keyword-3 | Topological states of matter |