Density-Matrix Embedding Theory Study of the One-Dimensional Hubbard–Holstein Model

Journal Of Chemical Theory And Computation 15 (4), 2221 - 2232 (2019)

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

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.

Additional Information

Preprint - 2.93 MB
We would like to acknowledge helpful discussions with Garnet K. Chan. C.H. acknowledges funding through ERC Grant No. 742102 QUENOCOBA. M.A.S. acknowledges financial support by the DFG through the Emmy Noether programme (SE 2558/ 2-1). T.E.R. is grateful for the kind hospitality of Princeton University, where a part of this project was carried out. U.M. acknowledges funding by the IMPRS-UFAST. A.R. acknowledges financial support by the European Research Council (ERC-2015-AdG-694097). The Flatiron Institute is a division of the Simons Foundation.

Related Projects

Related Research Areas