Properties of the half-filled Hubbard model investigated by the strong coupling diagram technique

TL;DR

This paper uses the strong coupling diagram technique to analyze the half-filled Hubbard model, accurately capturing the Mott transition at a critical interaction strength and comparing spectral properties with Monte Carlo results.

Contribution

It provides a self-consistent solution for the electron Green's function in the Hubbard model at half-filling using the strong coupling diagram technique, identifying the Mott transition point and validating results against Monte Carlo simulations.

Findings

Mott transition at $U_c \\approx 6.96t$

Spectral functions agree with Monte Carlo for $U>U_c$

Qualitative accuracy in spectral features for $U<U_c$

Abstract

The equation for the electron Green's function of the fermionic Hubbard model, derived using the strong coupling diagram technique, is solved self-consistently for the near-neighbor form of the kinetic energy and for half-filling. In this case the Mott transition occurs at the Hubbard repulsion $U_c\approx 6.96t$, where $t$ is the hopping constant. The calculated spectral functions, density of states and momentum distribution are compared with results of Monte Carlo simulations. A satisfactory agreement was found for $U>U_c$ and for temperatures, at which magnetic ordering and spin correlations are suppressed. For $U<U_c$ and lower temperatures the theory describes qualitatively correctly positions and widths of spectral continua, variations of spectral shapes and occupation numbers with changing wave vector and repulsion. The locations of spectral maxima turn out to be close to the positions of $\delta$-function peaks in the Hubbard-I approximation.