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arXiv · 1811.00048

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

Teresa E. Reinhard·Uliana Mordovina·Claudius Hubig·Joshua S. Kretchmer·Ulrich Schollwöck·Heiko Appel·Michael A. Sentef·Angel Rubio
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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 excellent agreement of the resulting phase boundaries. We also compare the fully 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.

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Teresa E. Reinhard, Uliana Mordovina, Claudius Hubig, Joshua S. Kretchmer, Ulrich Schollwöck, Heiko Appel, Michael A. Sentef, Angel Rubio. 2018-10-31. Density-matrix embedding theory study of the one-dimensional Hubbard-Holstein model. https://doi.org/10.1021/acs.jctc.8b01116

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