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Reinhard, Teresa E.; Mordovina, Uliana; Hubig, Claudius; Kretchmer, Joshua S.; Schollwöck, Ulrich; Appel, Heiko; Sentef, Michael A.; Rubio, Angel (2019): Density-Matrix Embedding Theory Study of the One-Dimensional Hubbard-Holstein Model. In: Journal of Chemical Theory and Computation, Vol. 15, No. 4: pp. 2221-2232
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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 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.