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Systematic construction of density functionals based on matrix product state computations

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Lubasch,  Michael
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;
Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK;

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Appel,  Heiko
Theory, Fritz Haber Institute, Max Planck Society;
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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Rubio,  Angel
Theory, Fritz Haber Institute, Max Planck Society;
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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Cirac,  J. Ignacio
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;

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Bañuls,  Mari-Carmen
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;

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njp_18_8_083039.pdf
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Citation

Lubasch, M., Fuks, J. I., Appel, H., Rubio, A., Cirac, J. I., & Bañuls, M.-C. (2016). Systematic construction of density functionals based on matrix product state computations. New Journal of Physics, 18(8): 083039. doi:10.1088/1367-2630/18/8/083039.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002B-3027-B
Abstract
We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz whose non-locality can be increased systematically. Second, we present a fitting strategy that is based on systematically increasing a reasonably chosen set of training densities. We investigate our procedure in the context of strongly correlated fermions on a one-dimensional lattice in which we compute accurate training densities with the help of matrix product states. Focusing on the exchange-correlation energy, we demonstrate how an efficient approximation can be found that includes and systematically improves beyond the local density approximation. Importantly, this systematic improvement is shown for target densities that are quite different from the training densities.