# Gutzwiller projection for exclusion of holes: Application to strongly correlated Ionic Hubbard Model and Binary Alloys

## TL;DR

This paper develops a Gutzwiller projection framework for systems where holes or doublons are selectively projected out, applying it to the ionic Hubbard model and binary alloys to analyze strongly correlated electron behavior.

## Contribution

It introduces a novel Gutzwiller approximation for hole projection, extending the formalism to systems with site-dependent projections in strongly correlated models.

## Key findings

- Derived effective low energy Hamiltonians for ionic Hubbard model and binary alloys.
- Generalized Gutzwiller approximation factors for site-specific projections.
- Analyzed the impact of selective hole and doublon projections on system properties.

## Abstract

We consider strongly correlated limit of variants of the Hubbard model (HM) in which on parts of the system it is energetically favourable to project out doublons from the low energy Hilbert space while on other sites of the system it is favourable to project out holes while still allowing for doublons. As an effect the low energy Hilbert space itself varies with sites of the system. Though the formalism is well developed for the case of doublon projection in the literature, case of hole projection has not been explored in detail so far. We derive basic framework by defining creation and annihilation operators for electrons in a restricted Hilbert space where holes are projected out but which still allows for doublons. We generalise the idea of Gutzwiller approximation for case of hole projection which has been done in literature for the case of doublon projection. To be specific, we provide detailed analysis of strongly correlated limit of the ionic Hubbard model (IHM) which has a staggered potential $\Delta$ on two sublattices of a bipartite lattice and the correlated binary alloys which have binary disorder $\pm V/2$ randomly distributed on sites of the lattice. In both the cases, for $\Delta \sim U \gg t$ and for $V\sim U \gg t$, where $U$ is the Hubbard energy cost for having a doublon at a site, there are sites on which doublons are allowed while holes are the maximum energy states. We do a systematic generalization of similarity transformation for both these cases and obtain the effective low energy Hamiltonian. We further derive Gutzwiller approximation factors which provide renormalization of various terms in the effective low energy Hamiltonian due to the Gutzwiller projection operators, excluding holes on some sites and doublons on the remaining sites.