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arXiv · 2603.11463

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

Shariful Islam·Joel Bierman·Yuan Liu
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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.

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Shariful Islam, Joel Bierman, Yuan Liu. 2026-03-12. Bootstrap Embedding for Interacting Electrons in Phonon Coherent-state Mean Field. https://doi.org/10.1063/5.0320786

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