Charge density wave solutions of the Hubbard model in the composite operator formalism

TL;DR

This paper explores charge density wave phases in the Hubbard model using a composite operator formalism, revealing stable unidirectional density waves with specific periods and their evolution with doping, relevant to underdoped cuprates.

Contribution

It introduces a real space composite operator approach to study charge density waves in the Hubbard model, capturing the effects of strong correlations and disorder.

Findings

Multiple unidirectional charge-ordered states are stabilized within certain doping ranges.

Charge density waves with periods of 3 to 8 lattice spacings are energetically less favorable than larger periods.

Disorder induces short-range charge modulations and merging of Mott regions.

Abstract

We investigate the charge density wave phase in the strongly correlated Hubbard model without any other broken symmetry phase. Starting from the atomic Hamiltonian with no hopping, we generate quasiparticle operators corresponding to holons and doublons in the strongly correlated limit of the repulsive Hubbard model. We develop a real space composite operator formalism using the equation of motion technique to include the intersite hopping perturbatively. Our fully self-consistent calculation stabilizes multiple unidirectional translation symmetry broken states within the doping range $\delta=0.07$ to $0.2$. The charge-ordered states become increasingly unfavorable with hole-doping. The unidirectional density waves manifest as periodic modulations of half-filled Mott regions separated by hole-rich regions. Notably, density wave solutions with periods of $3$ to $8$ lattice spacing remain energetically higher than those with larger periods. Quenched disorder on the charge-ordered states induces the merging of the Mott regions and, consequently, forms short-ranged charge modulations. The density of states shows signatures of strongly correlated Mott regions, potentially relevant to the physics of underdoped cuprates.