School of Physics, University of Hyderabad, Central University P. O., Hyderabad, 500046, Telangana, India.
Sci Rep. 2017 Jun 19;7(1):3774. doi: 10.1038/s41598-017-03985-2.
The Holstein-Hubbard model with Gaussian phonon anharmonicity is studied in one-dimension at half filling using a variational method based on a series of canonical transformations. A fairly accurate phonon state is chosen to average the transformed Holstein-Hubbard Hamiltonian to obtain an effective Hubbard model which is then solved using the exact Bethe - ansatz following Lieb and Wu to obtain the ground state energy, the average lattice displacement and the renormalized parameters. The Mott-Hubbard criterion, local spin moment and the von Neumann entropy (which is a measure of quantum entanglement) are calculated to determine the ground state phase diagram which shows that the width of the metallic phase flanked by the SDW and CDW phases increases with increasing anharmonicity at low and moderate values of anharmonicity but eventually saturates when the anharmonicity becomes substantially large.
采用基于一系列正则变换的变分方法，在一维满占据条件下研究了具有高斯声子非谐性的Holstein-Hubbard 模型。选择相当准确的声子态来平均变换后的 Holstein-Hubbard 哈密顿量，以获得有效 Hubbard 模型，然后使用 Lieb 和 Wu 的精确 Bethe - ansatz 来求解，以获得基态能量、平均晶格位移和重整化参数。计算莫特-哈伯德判据、局域自旋矩和冯·诺依曼熵（衡量量子纠缠的程度），以确定基态相图，结果表明，在低和中等非谐性值下，由 SDW 和 CDW 相夹在中间的金属相的宽度随着非谐性的增加而增加，但当非谐性变得相当大时，最终会饱和。
