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Charge-density-wave formation in the Edwards fermion-boson model at one-third band filling

We examine the ground-state properties of the one-dimensional Edwards spinless fermion transport model by means of large-scale density-matrix renormalization-group calculations. Determining the single-particle gap and the Tomonaga-Luttinger liquid parameter ($K_ρ$) at zero temperature, we prove the existence of a metal-to-insulator quantum phase transition at one-third band filling. The insulator---established by strong correlation in the background medium---typifies a charge density wave (CDW) that is commensurate with the band filling. $K_ρ=2/9$ is very small at the quantum critical point, and becomes $K_ρ^{\rm CDW}=1/9$ in the infinitesimally doped three-period CDW, as predicted by the bosonization approach.