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

Teresa E Reinhard,Claudius Hubig,Joshua S Kretchmer,Angel Rubio,Ulrich Schollwöck,Uliana Mordovina,Michael A Sentef,Heiko Appel

doi:10.1021/acs.jctc.8b01116

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.

Highlights

The interplay of competing interactions is a central theme of quantum many-body physics
In the one-dimensional Hubbard−Holstein model, three competing forces can be found: first, the electron hopping strength t, that leads to mobilization of the electrons and will put the system in a metallic phase; second, the electron−electron interaction U that, if dominant, leads to an immobilized spin wave for the electronic degrees of freedom, that is, a Mott phase; third, the electron−phonon coupling g that, if dominant, leads to a Peierls phase, which is the position of the electrons on the lattice if distorted from the initial position, forming a charge density wave
We discuss the results of our density-matrix embedding theory (DMET) calculation when solving the Hubbard−Holstein model Hamiltonian

Summary

INTRODUCTION

The interplay of competing interactions is a central theme of quantum many-body physics. NpNh− , 2Nimp similar to the electronic case, determine the dimension of the phononic Fock spaces on the impurity i and on the rest of the system j Due to their bosonic nature, the number of phononic basis functions is in principle indefinitely Nph = ∞. In the one-dimensional Hubbard−Holstein model, three competing forces can be found: first, the electron hopping strength t, that leads to mobilization of the electrons and will put the system in a metallic phase; second, the electron−electron interaction U that, if dominant, leads to an immobilized spin wave for the electronic degrees of freedom, that is, a Mott phase; third, the electron−phonon coupling g that, if dominant, leads to a Peierls phase, which is the position of the electrons on the lattice if distorted from the initial position, forming a charge density wave. We decide to discuss our results in terms of dimensionless coupling constants: u= U, g2 λ=

RESULTS

CONCLUSIONS AND OUTLOOK

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■ REFERENCES