Topological phases and entanglement in real space for 1D SSH topological insulator: effects of first and second neighbor-hoppings

TL;DR

This paper investigates how first and second neighbor hoppings in a 1D SSH topological insulator influence topological phases and entanglement, revealing that second-neighbor interactions increase entanglement and identifying conditions for maximally entangled states.

Contribution

It introduces a detailed analysis of entanglement and topological phase transitions in a 1D SSH model with extended hopping interactions, highlighting the role of second neighbors.

Findings

Second-neighbor hopping increases entanglement compared to first-neighbor hopping.

Critical points of maximal entanglement correspond to topological phase transitions.

Conditions for generating maximally entangled hybrid Bell states are established.

Abstract

The hybrid atoms-cell site entanglement in a one-dimensional Su-Schrieffer-Heeger (SSH) topological insulator with first and second neighbor hopping interaction in space representation of finite chains is analyzed. The geometric phase is calculated by the Resta electric polarization and the entanglement in the atomic basis by the Schmidt number. A relation between entanglement and the topological phase transitions (TPT) is given since the Schmidt number has critical points of maximal entangled (ME) states in the singularities of the geometrical phase. States with second-neighbors have higher entanglement than first-order hopping. The general conditions to produce ME hybrid Bell states and the localization-entanglement relation are given.