Max Planck Institute for the Structure and Dynamics of Matter , Luruper Chaussee 149 , Hamburg 22761 , Germany.
Max Planck Institute of Quantum Optics , Hans-Kopfermann-Str. 1 , Garching 85748 , Germany.
J Chem Theory Comput. 2019 Apr 9;15(4):2221-2232. doi: 10.1021/acs.jctc.8b01116. Epub 2019 Mar 12.
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.
我们提出了一种密度矩阵嵌入理论（DMET）研究一维 Hubbard-Holstein 模型，该模型是电子-电子和电子-声子相互作用相互作用的典范。通过分析单粒子激发能隙，我们发现了在缓慢声子的绝热条件下，直接从 Peierls 绝缘相到 Mott 绝缘相的转变，而在快速声子的反绝热条件下，存在相当大的金属相。我们对 DMET 的局域能量和激发能隙结果与密度矩阵重整化群（DMRG）结果进行了基准测试，并发现了相应相边界的良好一致性。我们还将完整的声子量子处理与标准 Born-Oppenheimer（BO）近似进行了比较。在绝热条件下，BO 近似与 DMET 给出了定性相似的结果，但在反绝热条件下完全失效，BO 预测从 Mott 到 Peierls 绝缘相的直接转变，而 DMET 则正确地显示了较大的金属相。这突出了在一维 Hubbard-Holstein 模型中声子自由度的量子涨落对金属性的重要性。
