Determination of the Fermi surface by charge density correlations

The Fermi surface topology plays a crucial role in the study of high-temperature superconductivity cuprates. The conventional method for determining the Fermi surface is the maximum spectral intensity method, which involves numerical analytical continuation of Matsubara data for the one-body Green's function. However, the numerical analytical continuation is sensitive to the noise or the precision of the Matsubara data, and hence is not always reliable. With this in mind, we propose a simple and specific notion as a reference for the Fermi surface. It is the derivative of the momentum distribution function nk with respect to the chemical potential mu. Our analysis of the noninteracting system shows that the momentum, at which dnk/d mu takes the maximum value, constitutes a surface, which coincides with the Fermi surface. The relationship between dnk/d mu and the Fermi surface in general cases is also analyzed. In order to numerically demonstrate this relationship, we calculate and compare on the two-dimensional Hubbard model within the HGW method. The results show that, at least in the weak and intermediate coupling regimes, using the notion of dnk/d mu to determine the Fermi surface is reliable. We further studied the cases with model parameters standing for realistic materials, and found the surface determined by dnk/d mu exhibits topological transition with the charge filling, similar to the Fermi surface in the cuprates. We believe that using the derivative of the momentum distribution function with respect to the chemical potential to determine the Fermi surface is a reasonable, efficient, and potentially valuable approach.