Department of Mathematics, Imperial College London, London SW7 2BZ, UK.
J Phys Condens Matter. 2010 Nov 3;22(43):435601. doi: 10.1088/0953-8984/22/43/435601. Epub 2010 Oct 7.
Holes in a Mott insulator are represented by spinless fermions in the fermion-boson model introduced by Edwards. Although the physically interesting regime is for low to moderate fermion density, the model has interesting properties over the whole density range. It has previously been studied at half-filling in the one-dimensional (1D) case by numerical methods, in particular using exact diagonalization and the density matrix renormalization group (DMRG). In the present study the one-particle Green's function is calculated analytically by means of a decoupling scheme for the equations of motion, valid for arbitrary density in 1D, 2D and 3D with fairly large boson energy and zero boson relaxation parameter. The Green's function is used to compute some ground state properties, and the one-fermion spectral function, for fermion densities n = 0.1, 0.5 and 0.9 in the 1D case. The results are generally in good agreement with numerical results obtained using the DMRG and dynamical DMRG, and new light is shed on the nature of the ground state at different fillings. The Green's function approximation is sufficiently successful in 1D to justify future application to the 2D and 3D cases.
在 Edwards 提出的费米子-玻色子模型中，Mott 绝缘体中的孔由无自旋费米子表示。尽管物理上有趣的区域是低到中等的费米子密度，但该模型在整个密度范围内都具有有趣的性质。以前已经通过数值方法，特别是使用精确对角化和密度矩阵重整化群（DMRG），在一维（1D）情况下的半填充情况下对其进行了研究。在本研究中，通过适用于 1D、2D 和 3D 中任意密度以及相当大的玻色子能量和零玻色子弛豫参数的运动方程的解耦方案，对单粒子格林函数进行了分析计算。格林函数用于计算一些基态性质，以及在 1D 情况下费米子密度 n = 0.1、0.5 和 0.9 的单费米子能谱函数。结果通常与使用 DMRG 和动态 DMRG 获得的数值结果非常吻合，并为不同填充下的基态性质提供了新的认识。格林函数近似在一维中非常成功，可以为未来在二维和三维情况下的应用提供依据。
