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

Teresa E Reinhard1, Uliana Mordovina1, Claudius Hubig2

  • 1Max Planck Institute for the Structure and Dynamics of Matter , Luruper Chaussee 149 , Hamburg 22761 , Germany.

Journal of Chemical Theory and Computation
|February 27, 2019
PubMed
Summary
This summary is machine-generated.

Density-matrix embedding theory reveals distinct phase transitions in the one-dimensional Hubbard-Holstein model. Quantum phonon effects are crucial for metallicity, unlike the Born-Oppenheimer approximation, especially in the anti-adiabatic regime.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Theory
  • Materials Science

Background:

  • The one-dimensional Hubbard-Holstein model is a key system for understanding electron-electron and electron-phonon interactions.
  • Accurate theoretical descriptions are needed to capture complex phase transitions and material properties.

Purpose of the Study:

  • To investigate the phase transitions in the one-dimensional Hubbard-Holstein model using Density-Matrix Embedding Theory (DMET).
  • To compare the performance of DMET with Density-Matrix Renormalization Group (DMRG) and the Born-Oppenheimer (BO) approximation.

Main Methods:

  • Density-Matrix Embedding Theory (DMET) was employed to study the Hubbard-Holstein model.
  • Results were benchmarked against Density-Matrix Renormalization Group (DMRG) calculations.
  • A comparison was made between full quantum phonon treatment and the Born-Oppenheimer (BO) approximation.

Main Results:

  • A direct Peierls insulator to Mott insulator transition was observed in the adiabatic regime (slow phonons).
  • A significant metallic phase was found in the anti-adiabatic regime (fast phonons), absent in the BO approximation.
  • DMET results for on-site energies and excitation gaps showed good agreement with DMRG, validating the phase boundaries.

Conclusions:

  • DMET accurately captures the phase diagram of the one-dimensional Hubbard-Holstein model, including crucial quantum phonon effects.
  • The Born-Oppenheimer approximation fails to describe the metallic phase in the anti-adiabatic regime, highlighting the importance of quantum fluctuations.
  • Quantum fluctuations of phonons are essential for understanding metallicity in this model system.