Fig. 4: The renormalized phonon dispersion.

a Ω(q, iν_n = 0) along the high-symmetry cuts of the first Brillouin zone, computed on an L = 10 lattice. As the temperature is lowered Ω(q, iν_n = 0) softens at the ordering wave-vector q = (π, π, π)a⁻¹, with other q remaining essentially pinned at Ω₀. The inset shows the softening of the Ω(q_cdw, 0) mode specifically versus β. b Ω(q, iν_n = 0) for different lattice sizes, measured at a fixed inverse temperature β = 12.5 eV⁻¹ below the transition temperature. Here, Ω(q, 0) softens at q_cdw for all lattice sizes L = 6, 8, and 10. The inset shows Ω(q_cdw, 0) decreasing with increasing lattice size, with the dashed line acting as a guide for the eye. The error bars in this figure are the standard deviation of the mean of our measurements.