Figure 6. Polaron energy-momentum relation.

This plot compares the shape of the energy-momentum curves for different models calculated with the electron–phonon coupling constant α_e−ph≃2.5. The energy is measured in units of the vibrational energy ħω₀ and the wave number in units of k_p=(2mω₀/ħ)^1/2. The dashed lines show the parabolic dispersion, for the bare band carrier (black) and for the polaronic carrier with renormalized mass m_p (blue). The solid lines display the non-parabolic dispersion obtained with variational calculations, according to Lee–Low–Pines theory¹¹,³⁰ (green curve) and according to Larsen theory¹³,³¹ (red curve). The latter is shown in the limited range of its applicability, but it is this type of the dispersion that was actually confirmed in the state-of-the-art diagrammatic Monte-Carlo calculations³².