# Topological quantum transition driven by charge-phonon coupling in the Haldane Chern insulator

## TL;DR

This paper demonstrates that charge-phonon coupling can induce a topological quantum transition in the Haldane Chern insulator, changing it from a topological to a trivial phase, with observable signatures in fermion occupancy and phonon spectra.

## Contribution

It provides the first evidence that charge-phonon interactions can drive topological phase transitions in the Haldane model, revealing new mechanisms for topological control.

## Key findings

- Charge-phonon coupling drives the transition from topological to trivial insulator.
- Fermion occupancy at the Dirac point exhibits a discontinuity at the transition.
- Phonon propagator shows a two-peak structure indicating the transition.

## Abstract

In condensed matter physics many features can be understood in terms of their topological properties. Here we report evidence of a topological quantum transition driven by the charge-phonon coupling in the spinless Haldane model on a honeycomb lattice, a well-known prototypical model of Chern insulator. Starting from parameters describing the topological phase in the bare Haldane model, we show that the increasing of the strength of the charge lattice coupling drives the system towards a trivial insulator. The average number of fermions in the Dirac point, characterized by the lowest gap, exhibits a finite discontinuity at the transition point and can be used as direct indicator of the topological quantum transition. Numerical simulations show, also, that the renormalized phonon propagator exhibits a two peak structure across the quantum transition, whereas, in absence of the mass term in the bare Hadane model, there is indication of a complete softening of the effective vibrational mode signaling a charge density wave instability.