Phase separation and electron pairing in repulsive Hubbard clusters

TL;DR

This study uses exact calculations on small Hubbard clusters to explore phase separation, pairing fluctuations, and competing phases, providing insights into electron pairing mechanisms relevant to high-temperature superconductors.

Contribution

It presents the first exact thermal analysis of small Hubbard clusters revealing phase diagrams with pairing fluctuations and potential pairing mechanisms beyond half filling.

Findings

Identification of pairing fluctuations below a critical U$_c$(T)

Evidence of competing paired and unpaired phases

Support for electron pairing mechanisms in doped cuprates

Abstract

Exact thermal studies of small (4-site, 5-site and 8-site) Hubbard clusters with local electron repulsion yield intriguing insight into phase separation, charge-spin separation, pseudogaps, condensation, in particular, pairing fluctuations away from half filling (near optimal doping). These exact calculations, carried out in canonical (i.e. for fixed electron number N) and grand canonical (i.e. fixed chemical potential $\mu$) ensembles, monitoring variations in temperature T and magnetic field h, show rich phase diagrams in a T-$\mu$ space consisting of pairing fluctuations and signatures of condensation. These electron pairing instabilities are seen when the onsite Coulomb interaction U is smaller than a critical value U$_c$(T) and they point to a possible electron pairing mechanism. The specific heat, magnetization, charge pairing and spin pairing provide strong support for the existence of competing (paired and unpaired) phases near optimal doping in these clusters as observed in recent experiments in doped La$_{2-x}$Sr$_x$CuO$_{4+y}$ high T$_c$ superconductors.