Electronic Correlations within Fermionic Lattice Models

TL;DR

This paper explores two-site electronic correlations in a generalized Hubbard model, revealing how competing magnetic and superconducting interactions depend on energy levels and occupation, offering insights into phase diagrams of fermionic lattice systems.

Contribution

It introduces a detailed analysis of two-site correlations in a generalized Hubbard model, including intersite interactions and Cooper pair hopping, highlighting the universal competition between magnetism and superconductivity.

Findings

Generalized t-J interactions appear at different energy levels.

Competition between ferromagnetism, antiferromagnetism, and superconductivity persists even without Coulomb interactions.

The model's phase diagram is explained by the occupation-dependent activity of various interactions.

Abstract

We investigate two-site electronic correlations within generalized Hubbard model, which incorporates the conventional Hubbard model (parameters: $t$ (hopping between nearest neighbours), $U$ (Coulomb repulsion (attraction)) supplemented by the intersite Coulomb interactions (parameters: $J^{(1)}$(parallel spins), $J^{(2)}$ (antiparellel spins)) and the hopping of the intrasite Cooper pairs (parameter: $V$). As a first step we find the eigenvalues $E_{\alpha} $ and eigenvectors $|E_{\alpha}>$ of the dimer and we represent each partial Hamiltonian $E_{\alpha} |E_{\alpha} > < E_{\alpha} |$ ($\alpha =1,2,..,16$) in the second quantization with the use of the Hubbard and spin operators. Each dimer energy level possesses its own Hamiltonian describing different two-site interactions which can be active only in the case when the level will be occupied by the electrons. A typical feature is the appearence of two generalized $t-J$ interactions ascribed to two different energy levels which do not vanish even for $% U=J^{(1)}=J^{(2)}=V=0$ and their coupling constants are equal to $\pm t$ in this case. The competition between ferromagnetism, antiferromagnetism and superconductivity (intrasite and intersite pairings) is also a typical feature of the model because it persists in the case $U=J^{(1)}=J^{(2)}=V=0$ and $t\neq 0$. The same types of the electronic, competitive interactions are scattered between different energy levels and therefore their thermodynamical activities are dependent on the occupation of these levels. It qualitatively explains the origin of the phase diagram of the model. We consider also a real lattice as a set of interacting dimers to show that the competition between magnetism and superconductivity seems to be universal for fermonic lattice models.