An exact study of charge-spin separation, pairing fluctuations and pseudogaps in four-site Hubbard clusters

TL;DR

This paper provides an exact analysis of charge-spin separation, pairing fluctuations, and pseudogaps in four-site Hubbard clusters, revealing critical parameters for electron localization, pairing mechanisms, and phase diagrams akin to high-temperature superconductors.

Contribution

It offers a novel exact study combining eigenvalues with ensemble approaches to explore phase transitions and pseudogaps in small Hubbard clusters.

Findings

Identification of a critical U_c(T) for electron localization.

Existence of pairing gaps and pairing instability near N=3.

Phase diagram resembling high T_c cuprates with charge and spin pseudogaps.

Abstract

An exact study of charge-spin separation, pairing fluctuations and pseudogaps is carried out by combining the analytical eigenvalues of the four-site Hubbard clusters with the grand canonical and canonical ensemble approaches in a multidimensional parameter space of temperature (T), magnetic field (h), on-site interaction (U) and chemical potential. Our results, near the average number of electrons <N>=3, strongly suggest the existence of a critical parameter U_{c}(T) for the localization of electrons and a particle-hole binding (positive) gap at U>U_{c}(T), with a zero temperature quantum critical point, U_{c}(0)=4.584. For U<U_{c}(T), particle-particle pair binding is found with a (positive) pairing gap. The ground state degeneracy is lifted at U>U_c(T) and the cluster becomes a Mott-Hubbard like insulator due to the presence of energy gaps at all (allowed) integer numbers of electrons. In contrast, for U< U_c(T), we find an electron pair binding instability at finite temperature near <N>=3, which manifests a possible pairing mechanism, a precursor to superconductivity in small clusters. In addition, the resulting phase diagram consisting of charge and spin pseudogaps, antiferromagnetic correlations, hole pairing with competing hole-rich (<N>=2), hole-poor (<N>=4) and magnetic (<N>=3) regions in the ensemble of clusters near 1/8 filling closely resembles the phase diagrams and inhomogeneous phase separation recently found in the family of doped high T_c cuprates.