Bootstrap Embedding for Interacting Electrons in Phonon Coherent-state Mean Field

TL;DR

This paper introduces a bootstrap embedding framework for simulating interacting electrons coupled with phonons, demonstrating efficiency and accuracy in localized regimes and scalability to large systems.

Contribution

The development of a combined bootstrap embedding and coherent-state mean-field method for electron-phonon systems, enabling large-scale and efficient simulations.

Findings

Accurate modeling of large 1D Hubbard-Holstein systems up to 350 sites.

Significant runtime advantage over DMRG for small systems.

Effective in localized regimes like Mott insulators and strong-coupling polarons.

Abstract

We develop a fermi-bose bootstrap embedding (fb-BE) framework for the ground state of interacting elec- trons coupled to phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron-phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for frag- ment size and total system size are demonstrated for one-dimensional Hubbard-Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to infinite system size. Benchmarking against density matrix renormalization group for small 8-site system at half- and quarter-filling shows orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.