Khatami Ehsan, Perepelitsky Edward, Rigol Marcos, Shastry B Sriram
Department of Physics, University of California, Santa Cruz, California 95064, USA and Department of Physics, University of California, Davis, California 95616, USA.
Department of Physics, University of California, Santa Cruz, California 95064, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):063301. doi: 10.1103/PhysRevE.89.063301. Epub 2014 Jun 2.
We implement a highly efficient strong-coupling expansion for the Green's function of the Hubbard model. In the limit of extreme correlations, where the onsite interaction is infinite, the evaluation of diagrams simplifies dramatically enabling us to carry out the expansion to the eighth order in powers of the hopping amplitude. We compute the finite-temperature Green's function analytically in the momentum and Matsubara frequency space as a function of the electron density. Employing Padé approximations, we study the equation of state, Kelvin thermopower, momentum distribution function, quasiparticle fraction, and quasiparticle lifetime of the system at temperatures lower than, or of the order of, the hopping amplitude. We also discuss several different approaches for obtaining the spectral functions through analytic continuation of the imaginary frequency Green's function, and show results for the system near half filling. We benchmark our results for the equation of state against those obtained from a numerical linked-cluster expansion carried out to the eleventh order.
我们为哈伯德模型的格林函数实现了一种高效的强耦合展开。在极端关联的极限情况下，即在位相互作用为无穷大时，图的计算显著简化，使我们能够将展开进行到跳跃幅度幂次的八阶。我们在动量和虚时频率空间中解析地计算有限温度格林函数，它是电子密度的函数。利用帕德近似，我们研究了温度低于或约为跳跃幅度时系统的状态方程、开尔文热功率、动量分布函数、准粒子分数和准粒子寿命。我们还讨论了通过虚频率格林函数的解析延拓获得谱函数的几种不同方法，并给出了接近半填充时系统的结果。我们将状态方程的结果与通过数值链接簇展开到十一阶得到的结果进行了基准比较。
