论文标题
Hartree-fock搭配Nambu纺纱器和2D哈伯德模型中的D-Wave冷凝
Hartree-Fock with Nambu spinors, and d-wave condensation in the 2D Hubbard model
论文作者
论文摘要
Hubbard模型通常的Hartree-fock近似是基于电子数量运算符的本征态。但是这种表述不是唯一的。根据NAMBU两组分旋转器配制的不同（和不相等）版本基于旋转和旋转电子数量之间差异的本征状态，其电子密度取决于$ u，t，t'$和化学势$μ$。该公式的优点是可以直接计算电子配对冷凝物。我们表明，在基线状态下，在此“ Nambu” Hartree-fock近似中获得的半填充，离散的旋转对称性自发折断，冷凝水在动量空间中表现出预期的D-WAVE形式。我们还表明，在大型$ u/t $和半填充的情况下，在此配方中获得了Mott绝缘器电子构型，并在局部抗fiferromagnetism和Stripe/域中的区域之间大致地定位边界，并将其定位在孔掺杂$ -$ -U/T $平面中。
The usual Hartree-Fock approximation to the Hubbard model is based on eigenstates of the electron number operator. But this formulation is not unique. A different (and inequivalent) version, formulated in terms of Nambu two-component spinors, is based on eigenstates of the difference between the numbers of spin up and spin down electrons, with electron density dependent on parameters $U,t,t'$ and chemical potential $μ$. The advantage of this formulation is that electron pairing condensates can be directly computed. We show that in the ground states away from half-filling, obtained in this "Nambu" Hartree-Fock approximation, a discrete rotation symmetry is spontaneously broken, and the condensates exhibit the expected d-wave form in momentum space. We also show that the Mott insulator electron configuration is obtained in this formulation at large $U/t$ and half-filling, and roughly locate the boundary, in the hole doping$-$$U/t$ plane, between a region of local antiferromagnetism and stripe/domain formation, and the region of d-wave condensation.
