Charge density waves (CDWs), spontaneous modulations of charge and lattice, are one of the fundamental orders in condensed matter systems. Since the modulation period of CDW strongly modifies the electronic structure and influences other emergent orders, unraveling the mechanism responsible for the periodicity is one of the major challenges in controlling quantum materials. While current phenomenological models based on the instability of the electronic structure have successfully described some of their characteristic features, the full complexity of CDW formation points to the energy landscape with much richer structures calling for additional or alternative underlying mechanisms. Here, we investigate the canonical CDW material $1\mathit{H}\text{−}{\mathrm{TaSe}}_2$, which undergoes multiple CDW phase transitions. By constructing a highly accurate interatomic potential trained on first-principles data, we achieved sub-meV-per-atom precision and reproduced the full experimental phase diagram, capturing discontinuous changes in modulation period and symmetry-breaking transitions. Based on these results, we construct an interacting eigenmode model that quantitatively accounts for the whole details using only a few low-energy eigenmodes and short-range anharmonic force constants. Our calculations clearly demonstrate that lattice anharmonicity is the primary driving mechanism for the complex evolution of CDW periodicity in transition-metal dichalcogenides. Our interacting eigenmode model further yields a simple condition governing whether CDWs in triangular and square lattices emerge uniaxially or as two-dimensionally.

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• Charge density waves
• Phase diagrams
• Phase transitions
• Transition metal dichalcogenides
• First-principles calculations