We extend the density matrix renormalization group to compute exact ground states of continuum many-electron systems in one dimension with long-range interactions. We find the exact ground state of a chain of 100 strongly correlated artificial hydrogen atoms. The method can be used to simulate 1D cold atom systems and to study density-functional theory in an exact setting. To illustrate, we find an interacting, extended system which is an insulator but whose Kohn-Sham system is metallic.

arXiv:1107.2394Physical Review LettersAug 1, 201287 citations

Bulletin of the American Physical Society

Exact density functionals for 1d systems

Lucas Wagner, Edwin Miles Stoudenmire, Kieron Burke, Steven White

Published Feb 27, 2012• 0 citations

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N

-electron system in

d

dimensions onto a single electron in $N\ifmmode\times\else\texttimes\fi{}d$ dimensions, properly symmetrized by the Young diagrams. We conclude that 1D LDA is of the same quality as its three-dimensional (3D) counterpart, and we infer conclusions about 3D LDA. The linear and nonlinear time-dependent responses of 1D model systems using LDA, exact exchange, and the exact solution are investigated and show very good agreement in both cases, except for the well-known problem of missing double excitations. Consequently, the 3D LDA is expected to be of good quality beyond the linear response. In addition, the 1D LDA should prove useful in modeling the interaction of atoms with strong laser fields, where this specific 1D model is often used.