A hybrid Monte Carlo study of bond-stretching electron–phonon interactions and charge order in BaBiO3

The relationship between electron-phonon ($e$-ph) interactions and charge-density-wave (CDW) order in the bismuthate family of high-temperature superconductors remains unresolved. We address this question using nonperturbative hybrid Monte Carlo calculations for parent compound BaBiO$_3$. Our model includes Bi $6s$ O $2p_\sigma$ orbitals coupling to Bi-O bond-stretching branch optical phonons via modulations hopping integral. simulate three-dimensional clusters up 4000 orbitals, with input parameters taken from {\it ab initio} electronic structure a phonon energy $\hbar\Omega_0 = 60$~meV. results demonstrate that modes is sufficient reproduce CDW transition system, despite relatively small dimensionless coupling. also find deviates weak-coupling Peierls' picture. This work demonstrates off-diagonal $e$-ph orbital space are vital establishing phase diagram.