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Density-matrix embedding theory study of the one-dimensional Hubbard-Holstein model

MPS-Authors
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Reinhard,  T.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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Mordovina,  U.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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Appel,  H.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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Sentef,  M. A.
Theoretical Description of Pump-Probe Spectroscopies in Solids, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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Rubio,  A.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Computational Quantum Physics (CCQ), Flatiron Institute;

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acs.jctc.8b01116.pdf
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Citation

Reinhard, T., Mordovina, U., Hubig, C., Kretchmer, J. S., Schollwöck, U., Appel, H., et al. (2019). Density-matrix embedding theory study of the one-dimensional Hubbard-Holstein model. Journal of Chemical Theory and Computation, 15(4), 2221-2232. doi:10.1021/acs.jctc.8b01116.


Cite as: http://hdl.handle.net/21.11116/0000-0002-A4D9-0
Abstract
We present a density-matrix embedding theory (DMET) study of the one-dimensional Hubbard–Holstein model, which is paradigmatic for the interplay of electron–electron and electron–phonon interactions. Analyzing the single-particle excitation gap, we find a direct Peierls insulator to Mott insulator phase transition in the adiabatic regime of slow phonons in contrast to a rather large intervening metallic phase in the anti-adiabatic regime of fast phonons. We benchmark the DMET results for both on-site energies and excitation gaps against density-matrix renormalization group (DMRG) results and find good agreement of the resulting phase boundaries. We also compare the full quantum treatment of phonons against the standard Born–Oppenheimer (BO) approximation. The BO approximation gives qualitatively similar results to DMET in the adiabatic regime but fails entirely in the anti-adiabatic regime, where BO predicts a sharp direct transition from Mott to Peierls insulator, whereas DMET correctly shows a large intervening metallic phase. This highlights the importance of quantum fluctuations in the phononic degrees of freedom for metallicity in the one-dimensional Hubbard–Holstein model.