Variational Polaron Theory for Ground States of Strongly Coupled Light-Matter and Electron-Phonon Systems
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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BibTeX
@misc{phuc2026variational,
title = {{Variational Polaron Theory for Ground States of Strongly Coupled Light-Matter and Electron-Phonon Systems}},
author = {Nguyen Thanh Phuc},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.19748},
eprint = {2606.19748},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.19748},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Variational Polaron Theory for Ground States of Strongly Coupled Light-Matter and Electron-Phonon Systems
AU - Nguyen Thanh Phuc
PY - 2026
DA - 2026/06/18
PB - arXiv
DO - 10.48550/arxiv.2606.19748
UR - https://arxiv.org/abs/2606.19748
AB - 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.
ER -