Exact analytical edge states in the extended Su-Schrieffer-Heeger model

• URL: http://arxiv.org/abs/2604.20561v1
• Date: Wed, 22 Apr 2026 13:43:32 GMT
• Title: Exact analytical edge states in the extended Su-Schrieffer-Heeger model
• Abstract summary: We investigate the topology of the different phases of the extended Su-Schrieffer-Heeger (eSSH) model.<n>For finite chains, we obtain analytical, approximate expressions for the low-energy edge states, which are shown to be highly accurate.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the topology of the different phases of the extended Su-Schrieffer-Heeger (eSSH) model, which includes hopping processes between translationally inequivalent atoms beyond nearest neighbors. Exact analytical expressions for the edge states of a semi-infinite eSSH chain are derived, with wave functions that decay exponentially from the boundary with a unit-cell decay factor z. From the winding number of the bulk Hamiltonian under periodic boundary conditions, we determine the topological phase diagram and establish the bulk-boundary correspondence: changes in the winding number coincide with bulk gap closings and with the condition |z|=1 for the edge-state solutions. For finite chains, we further obtain analytical, approximate expressions for the low-energy edge states, which are shown to be highly accurate.

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