Phase separation and electron pairing in repulsive Hubbard clusters

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.Comment: 5 pages, 5 figure

Possible phase separation in square and honeycomb Hubbard model: A variational cluster study

“…This physical picture manifests the presence of a microscopic inhomogeneity, which achieves a lower total free energy than that of a uniform electron distribution. This result is similar to what our group [13][14][15][16][17] has predicted using calculations for isolated Hubbard clusters. For example, an ensemble of bipartite 2 × 2 square and 2 × 4 ladder clusters has a tendency to phase separation at moderate on-site Coulomb interaction when the energy of a mixture of electronic states with N and N − 2 electron configurations becomes lower than that of a pure two states with N − 1 electrons.…”

“…[18] using the DCA. However, in our previous study of isolated clusters [13][14][15][16][17], we found that the abrupt change of density in Fig. 2 decreases by increasing temperature.…”

“…However, full diagonalization is still possible within relatively small Hubbard clusters such as squares, 8-site 2 × 4 ladders, two-dimensional Betts cells and pyramids [34,35]. The problem of a quantum gas of interacting many electrons in independent clusters is exactly solvable in the ground state and at finite temperatures [13][14][15][16][17]. The canonical and grand canonical ensembles in equilibrium display thermodynamic phase diagrams and the tendency to phase separation through responses of the system to changes of electron concentration and magnetic field.…”

“…The importance of electronic phase separations driven by electron correlations was realized in the Hubbard model by Visscher [10] in the 1970s and was systematically studied at the strong interaction limit later using the t-J model [11,12]. Our recent many-body calculations in different bipartite and non-bipartite clusters on phase separation in the Hubbard model are based on exact diagonalization [13][14][15][16][17]. These results at some critical Coulomb interactions display a level crossing instabilities similar to phase separation transitions seen at various doping levels even close to the optimal doping [1][2][3].…”

“…Macridin et al [18,19] proposed a thermodynamical description of electronic phase transition, and the theory further points to the existence of a quantum critical point which closely resembles the level crossing point observed near phase separation instability at the cluster level in Refs. [13][14][15]. Aichhorn et al [20,21] discussed the coexistence of the global antiferromagnetic and superconducting long-range orders in variational cluster calculations.…”