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

Journal of Chemical Theory and Computation
Teresa E ReinhardAngel Rubio

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.

References

Nov 9, 1992·Physical Review Letters·S R White
Oct 4, 2005·Physical Review Letters·R T Clay, R P Hardikar
Oct 13, 2007·Physical Review Letters·Philipp Werner, Andrew J Millis
Apr 7, 2010·Physical Review Letters·Fabrice P LaussyIvan A Shelykh
Dec 12, 2012·Physical Review Letters·Gerald Knizia, Garnet Kin-Lic Chan
Mar 12, 2013·Journal of Chemical Theory and Computation·Gerald Knizia, Garnet Kin-Lic Chan
May 11, 2019·Physical Review Letters·Jonathan B CurtisVictor M Galitski

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Citations

Dec 16, 2020·The Journal of Chemical Physics·Alec F WhiteGarnet Kin-Lic Chan
Dec 10, 2019·Journal of Chemical Theory and Computation·Hung Q PhamLaura Gagliardi
Nov 30, 2021·The Journal of Physical Chemistry Letters·Abhishek MitraLaura Gagliardi

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Software Mentioned

DMET
DMRG
SyTen

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