二维哈伯德模型中Hartree-Fock基态的自旋和电荷密度波
Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model
摘要：
在非限制性Hartree-Fock（UHF）理论下研究了二维排斥哈伯德模型的基态.磁性和电荷性质是由系统的，大规模的，精确的数值计算，并量化为电子掺杂$h$的函数。在求解自洽UHF方程时，采用多初始组态和模拟退火算法，以利于收敛到全局最小值。采用新的方法，以尽量减少有限尺寸的影响，以达到热力学极限。在低到中等的相互作用强度和低掺杂下，UHF基态是线性自旋密度波（l-SDW），具有反铁磁序和调制波。调制波的波长为$2/h$。相应的电荷序存在，但比自旋序弱得多，因此空穴是可移动的。随着相互作用的增加，l-SDW态演化成几个不同的相，空穴最终变得局域化。提出了一个简单的配对模型，并对低相互作用强度和小掺杂进行了解析计算，以帮助理解数值结果，并为SDW基态的性质提供了物理图像。通过与最近的多体计算的比较，它表明，对于中间相互作用，超高频解决方案提供了一个很好的描述磁关联在真正的基态的哈伯德模型。
英文摘要：
The ground states of the two-dimensional repulsive Hubbard model are studied within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge properties are determined by systematic, large-scale, exact numerical calculations, and quantified as a function of electron doping $h$. In the solution of the self-consistent UHF equations, multiple initial configurations and simulated annealing are used to facilitate convergence to the global minimum. New approaches are employed to minimize finite-size effects in order to reach the thermodynamic limit. At low to moderate interacting strengths and low doping, the UHF ground state is a linear spin-density wave (l-SDW), with antiferromagnetic order and a modulating wave. The wavelength of the modulating wave is $2/h$. Corresponding charge order exists but is substantially weaker than the spin order, hence holes are mobile. As the interaction is increased, the l-SDW states evolves into several different phases, with the holes eventually becoming localized. A simple pairing model is presented with analytic calculations for low interaction strength and small doping, to help understand the numerical results and provide a physical picture for the properties of the SDW ground state. By comparison with recent many-body calculations, it is shown that, for intermediate interactions, the UHF solution provides a good description of the magnetic correlations in the true ground state of the Hubbard model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
