# A bridge between wave function methods and functional methods: Density matrix embedding theory for coupled fermion-boson systems

Teresa Reinhard, Max Planck Institut für Struktur und Dynamik der Materie, Hamburg

23.11.2016 at 14:00

In a very general sense, there are two kinds of ways to describe quantum many-body systems: Wave function methods and functional methods. While wave function methods yield very accurate results and have convergable error bars, they do not bypass the exponential wall of many-body physics. Instead of directly describing the wave function, we can map it onto a lower dimensional object and describe all physical properties in terms of this object. In Density Functional Theory (DFT) for instance, this object is the (electronic) density. While with this technique we can describe three-dimensional realistic systems, we have to approximate the mapping between wave function and density. Within present DFT-methodologies, such approximations cannot be improved in a systematic way.

Density matrix embedding theory (DMET) is a new technique that benefits from "the best of both worlds". Using the Schmidt decomposition, one can divide the system into an impurity and a bath region. While describing the impurity region exactly, one can project the bath onto the part of the Hilbert space that contains the entanglement with the impurity region. This entangled bath, together with the impurity region, has to be solved exactly. By comparing the reduced one particle density of the correlated and a mean field system, which yields the first guess for the projection, one can improve the projection self-consistently.

DMET has been developed by the Chan group in recent years [1] and can be applied to electronic lattice, as well as molecular systems [2]. In the present work we generalize this technique to coupled electron-boson systems, which enables us to describe coupled electron-phonon as well as electron-photon systems. As a first step we apply this new approach to the Hubbard-Holstein-Hamiltonian.

[1] G. Knizia, G. K.-L Chan, Phys. Rev. Lett 109, 186404, (2012)

[2] S. Wouters, C. A. Jimnez-Hoyos, G. K.-L. Chan, arXiv:1605.05547 (2016)

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