Momentum distributions and Fermi surface in t-J model

Rajiv R. P. Singh, Rodney L. Glenister

We study the momentum distribution function n(k) for the two-dimensional t-J model by high-temperature expansions. Starting with a k-independent n(k) at T=\ensuremath{\infty}, we observe the buildup of a sharp Fermi-surface-like feature as the temperature is lowered. For very small density of electrons, our results are clearly consistent with Luttinger's theorem. At all fillings the contours of constant n(k) closely resemble those of the tight-binding model. No evidence for pocketlike Fermi surfaces is seen. Far from the Fermi surface n(k) has a particle-hole asymmetry similar to that found in the one-dimensional, U=\ensuremath{\infty} Hubbard model.

Satoshi Nishimoto, R. Eder, Y. Ohta

A. Ramšak, Igor Sega, Peter Prelovšek

Zhipeng Sun

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 ${n}_{\mathbit{k}}$ with respect to the chemical potential $\ensuremath{\mu}$. Our analysis of the noninteracting system shows that the momentum, at which $d{n}_{\mathbit{k}}/d\ensuremath{\mu}$ takes the maximum value, constitutes a surface, which coincides with the Fermi surface. The relationship between $d{n}_{\mathbit{k}}/d\ensuremath{\mu}$ 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 $d{n}_{\mathbit{k}}/d\ensuremath{\mu}$ 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 $d{n}_{\mathbit{k}}/d\ensuremath{\mu}$ 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.

Majid Modarres

The momentum distribution of nuclear matter n(k) is evaluated by using the cluster expansion for the occupation probability. The gap in n(k) at the Fermi surface is found to be about 0.96 compared with 1.0 for the noninteracting Fermi gas model. It is shown that the high-momentum tail of n(k) is very much smaller than it has been thought.