One- and two-particle properties of the weakly interacting two-dimensional Hubbard model in proximity to the van Hove singularity
One- and two-particle properties of the weakly interacting two-dimensional Hubbard model in proximity to the van Hove singularity
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DOI：
10.1103/physrevb.106.035145
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发表时间：
2022-03
影响因子：
3.7
通讯作者：
B. McNiven;H. Terletska;G. T. Andrews;J. LeBlanc
中科院分区：
文献类型：
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作者：
B. McNiven;H. Terletska;G. T. Andrews;J. LeBlanc
我们使用直接微扰方法研究了二维方格上 t − t (cid:48) − U Hubbard 模型的弱耦合极限。在符号计算工具的帮助下，我们计算了 χ ↑↑ 和 χ ↑↓ 基础上的纵向密度-密度相关函数，从中我们可以获得任意掺杂和温度下的动态自旋和电荷磁化率。我们发现，对于非零 t (cid:48) ，零频率相当的 q = ( π, π ) 自旋和电荷激发在不同密度下各自最强，并且我们观察到明显的行为变化，该变化似乎与微扰膨胀所基于的非相互作用色散的范霍夫奇点相关。我们发现范霍夫奇点附近的压缩性大大降低，并且双人居住中的行为也发生了变化。对于有限 t (cid:48) ，观察到的范霍夫奇点发生在远离半填充的地方，这使我们得出结论，这种可压缩性的降低与人们在强耦合状态下预期的莫特绝缘物理不同。我们计算了完整的动态自旋和电荷激发，并观察了电子和空穴掺杂场景的独特结构，与铜酸盐材料的实验一致。最后，我们观察到范霍夫奇点附近自旋和电荷激发的特殊分裂，其起源可以追溯到能带底部附近的分裂。
We study the weak-coupling limit of the t − t (cid:48) − U Hubbard model on a two-dimensional square lattice using a direct perturbative approach. Aided by symbolic computational tools, we compute the longitudinal density-density correlation functions in the χ ↑↑ and χ ↑↓ basis from which we can obtain the dynamical spin and charge susceptibilities at arbitrary doping and temperature. We find that for non-zero t (cid:48) , the zero frequency commensurate q = ( π, π ) spin and charge excitations are each strongest at different densities and we observe a clear behavioral change that appears tied to the van Hove singularity of the non-interacting dispersion upon which the perturbative expansion is built. We find a strongly reduced compressibility in the vicinity of the van Hove singularity as well as a behavioral change in the double occupancy. For finite t (cid:48) , the observed van Hove singularity occurs away from half-filling leading us to conclude that that this reduction in compressibility is distinct from Mott insulating physics that one expects in the strong-coupling regime. We compute the full dynamical spin and charge excitations and observe distinct structure for electron and hole doped scenarios in agreement with experiments on cuprate materials. Finally, we observe a peculiar splitting in spin and charge excitations in the vicinity of the van Hove singularity, the origin of which is traced to a splitting near the bottom of the band.