Quantum and classical thermal melting of generalized Wigner crystals

Motivated by the recent discovery of correlated insulating "generalized Wigner crystal" (GWC) states in hetero-bilayer transition metal dichalcogenides [Nature 587, 214 - 218 (2020), Nature 597, 650 - 654 (2021)], we address the question of their thermal melting. Specifically, we address the role of quantum effects on the transition temperature T_c, building on recent theoretical work [npj Quantum Materials, 10, 95 (2025)]. We perform both finite-temperature Lanczos and classical Monte Carlo calculations, incorporating perturbative quantum effects, on the experimentally relevant extended Hubbard model with a double-gate screened potential, over a wide range of densities and fillings. Our analysis demonstrates that quantum effects play a decisive role, substantially altering the melting behavior of GWCs relative to classical predictions for some fillings, highlighting the source of some of the previous discrepancies between experiment and theory. We provide a qualitative picture that clarifies that while quantum melting of GWCs naturally reduces their ground state order parameter, it does not always decrease the melting temperature; it can instead increase it. We construct a finite temperature quantum phase diagram and provide a general explanation for when an increase in T_c is expected.