Variational Polaron Theory for Ground States of Strongly Coupled Light-Matter and Electron-Phonon Systems

Nguyen Thanh Phuc

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arXiv · 2606.19748

Variational Polaron Theory for Ground States of Strongly Coupled Light-Matter and Electron-Phonon Systems

Nguyen Thanh Phuc

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Abstract

Strong light-matter and electron-phonon coupling generate ground states dressed by virtual bosonic excitations, making bare-state truncations and perturbative treatments unreliable in the ultrastrong-coupling regime. We introduce a nonperturbative variational ground-state framework based on a state-dependent polaron transformation, combined with a product-state ansatz and a second-order perturbative correction for residual matter-boson entanglement. We show that the optimized transformed frame becomes asymptotically decoupled at infinite coupling, because the leading linear coupling is canceled while off-diagonal matter transitions are suppressed by displaced-oscillator overlaps. The approach is asymptotically correct in both weak- and strong-coupling limits and remains accurate in the intermediate regime, where fixed polaron transformations are least reliable. Dicke-model benchmarks reproduce ground-state energies, fidelities, and the superradiant transition, with second-order energy errors below 0.2%. Holstein-model benchmarks yield errors below 0.5% and clarify how translational symmetry affects wave-function quality. This dressed-basis framework enables nonperturbative modeling of strongly coupled light-matter and electron-phonon systems.

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Nguyen Thanh Phuc. 2026-06-18. Variational Polaron Theory for Ground States of Strongly Coupled Light-Matter and Electron-Phonon Systems. https://arxiv.org/abs/2606.19748

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