Figure 7
Upper panel: Scaled density \(({\hat{D}}_{\rho })\) and wave function \(({\hat{D}}_{\psi })\) distances between i-LDA and exact systems versus confining potential strength k. Inset shows the density profile for unconfined k = 0 and strongly confined k = 8 systems. Intermediate panel: percentage error between exact and LDA relative energy: \(|(E-{E}_{k=0})-\)\(({E}^{LDA}-{E}_{k=0}^{LDA})/(E-{E}_{k=0})|\times 100\). Lower panel: Scaled potential distances (\({\hat{D}}_{v}^{A}\) and \({\hat{D}}_{v}^{B}\)) between i-LDA and exact systems, versus confining potential strength k. In all panels: U = 2, d = 8 and N = 2, with confining potential kx2 symmetric with respect to chain centre.
