Determination of Fermi surface by charge density correlations

TL;DR

This paper introduces a new method using momentum-dependent compressibility to determine the Fermi surface in the 2D Hubbard model, linking charge density correlations to Fermi surface topology, especially relevant for high-temperature superconductors.

Contribution

It proposes a novel approach to identify the Fermi surface via charge density correlations, bypassing the analytical continuation problem in theoretical studies.

Findings

The method accurately reproduces the Fermi surface in weakly and intermediate coupling regimes.

In the correlated regime, the surface shows pocket and arc features similar to high-temperature superconductors.

Establishes a connection between charge density fluctuations and Fermi surface topology.

Abstract

The Fermi surface topology in the two-dimensional Hubbard model is particularly relevant for the high-temperature superconductors, whereas its theoretical research encounters with the difficulty of the analytical continuation problem. To this end, we proposed the concept of the momentum-dependent compressibility, defined as the variation of the momentum distribution function with respect to the chemical potential. The surface determined by the maximum of the momentum-dependent compressibility is nearly identical to the Fermi surface in the weakly and intermediate coupling regions according to our numerical results. In the correlated region, this surface also exhibits pocket and arc features, just like the Fermi surface in high-temperature superconductors. Therefore, for theoretical studies, this surface can be used as an alternative to determine the underlying Fermi surface. Considering that the momentum-dependent compressibility is closely related to the charge density correlations, our work also shows a connection between the Fermi surface topology and the charge density fluctuations.