Quantum-Classical Modeling of Charge Density Wave Dynamics in Correlated Materials

Charge density wave (CDW) order has potential applications in ultrafast electronic devices and provides valuable insight into coexisting superconducting phases. The microscopic origin of CDW order in correlated materials, however, depends sensitively on the interplay between electronic structure and electron–phonon coupling. Recently, quantum–classical (QC) approaches have enabled non-perturbative simulations of electron–phonon dynamics, though so far limited to single-particle phenomena like excitons and polarons. To extend these methods beyond the single-particle picture, we integrate real-time tensor network simulations within a QC framework, enabling a systematic assessment of the trade-off between computational cost and accuracy in treating electron–electron interactions. As a central example, we apply this method to study charge-density-wave melting in a one-dimensional Hubbard–Holstein model. Remarkably, we identify a regime where strong electronic correlations stabilize persistent charge order distinct from a Peierls mechanism. The QC framework reproduces fully quantum benchmarks and captures the qualitative melting dynamics across a broad parameter range.