Figure 5
From: Artificial neural networks for density-functional optimizations in fermionic systems
Density profile for (a) a finite chain of size L = 40 and n = 0.8, (b) a localized impurity system, with L = 15, impurity strength V = 2t and n = 0.4, and (c) a harmonically confined chain with L = 40, harmonic curvature k = 0.01 and n = 0.8, while (d) shows the per-site ground-state energy as a function of the harmonic confinement curvature for chains of size L = 40 and n = 0.8. In all cases we adopted open boundary conditions, U = 1t and m ~ 0. The results are either exact DMRG or approximated DFT-LSDA, with one of the functionals: FN, FVC or ANN. The percentage deviations are obtained via \(100\times |({e}_{0}^{approx}-{e}_{0}^{exact})/{e}_{0}^{exact}|\) and D is the average percentage deviation.
