Compressibility enhancement in an almost staggered interacting Harper model

TL;DR

This paper investigates how repulsive interactions affect the compressibility of an almost staggered Harper model, considering spin and longer-range interactions, using Hartree-Fock and DMRG methods.

Contribution

It extends previous work by analyzing the effects of spin and longer-range interactions on compressibility in the Harper model with advanced computational methods.

Findings

Compressibility is enhanced by repulsive interactions.

Longer-range interactions weaken the compressibility enhancement.

Hartree-Fock approximation remains accurate due to the flatness of the central band.

Abstract

We discuss the compressibility in the almost staggered fermionic Harper model with repulsive interactions in the vicinity of half-filling. It has been shown by Kraus et al. [33] that for spinless electrons and nearest neighbors electron-electron interactions the compressibility in the central band is enhanced by repulsive interactions. Here we would like to investigate the sensitivity of this conclusion to the spin degree of freedom and longer range interactions. We use the Hartree-Fock (HF) approximation, as well as density matrix renormalization group (DMRG) calculation to evaluate the compressibility. In the almost staggered Harper model, the central energy band is essentially flat and separated from the other bands by a large gap and therefore, the HF approximation is rather accurate.In both cases the compressibility of the system is enhanced compare to the non-interacting case, although the enhancement is weaker due to the inclusion of Hubbard and longer ranged interactions.