Generic gauge fields in the Hubbard model: emergence of pairing interaction

The spin-rotationally invariant SU(2) approach to the Hubbard model is extended to accommodate the charge degrees of freedom. Both U(1) and SU(2) gauge transformation are useed to factorize the charge and spin contribution to the original electron operator in terms of the emergent gauge fields. It is shown that these fields play a similar role as phonons in the BCS theory: they provide the "glue" for fermion pairing. By tracing out gauge bosons the form of paired states is established and the role of antiferromagnetic correlations is explicated.Comment: 4+ page

Excitonic phase transition in the extended three-dimensional Falicov-Kimball model

We study the excitonic phase transition in a system of the conduction band electrons and valence band holes described by the three-dimensional (3D) extended Falicov-Kimball (EFKM) model with the tunable Coulomb interaction $U$ between both species. By lowering the temperature, the electron-hole system may become unstable with respect to the formation of the excitons, i.e, electron-hole pairs at temperature $T=T_{\Delta}$, exhibiting a gap $\Delta$ in the particle excitation spectrum. To this end we implement the functional integral formulation of the EFKM, where the Coulomb interaction term is expressed in terms of U(1) phase variables conjugate to the local particle number, providing a useful representation of strongly correlated system. The effective action formalism allows us to formulate a problem in the phase-only action in the form of the quantum rotor model and to obtain analytical formula for the critical lines and other quantities of physical interest like charge gap, chemical potential and the correlation length.Comment: 27 pages, 15 figures (in the arXive version), 37 pages and 15 figures (in the published version

Effective pairing interaction in the two-dimensional Hubbard model within a spin rotationally invariant approach

We implement the rotationally-invariant formulation of the two-dimensional Hubbard model, with nearest-neighbors hopping $t$, which allows for the analytical study of the system in the low-energy limit. Both U(1) and SU(2) gauge transformations are used to factorize the charge and spin contributions to the original electron operator in terms of the corresponding gauge fields. The Hubbard Coulomb energy $U$ term is then expressed in terms of quantum phase variables conjugate to the local charge and variable spin-quantization axis, providing a useful representation of strongly correlated systems. It is shown that these gauge fields play a similar role as phonons in the BCS theory: they act as the "glue" for fermion pairing. By tracing out gauge degrees of freedom, the form of paired states is established and the strength of the pairing potential is determined. It is found that the attractive pairing potential in the effective low-energy fermionic action is non-zero in a rather narrow range of $U/t$.Comment: 12 pages, 1 figur

Requirement of focal adhesion kinase in branching tubulogenesis

We previously demonstrated that α3β1 integrins are essential to hepatocyte growth factor (HGF)-independent branching tubulogenesis in Mardin-Darby Canine Kidney (MDCK) cells. However, the involvement of integrin downstream signaling molecules remains unclear. In the present study, we successfully isolated cell lines possessing different tubulogenic potentials from the MDCK cells; cyst clones (CA4, CA6) forming cystic structures when cultured in 0.3% type I collagen gel and mass clones (M610, M611, M612) forming aggregated masses. Cyst clones maintained cystic structure in 0.1% collagen gel, whereas mass clones spontaneously developed into tubules. Both clones exhibited various morphologies when cultured on a dish: cyst clones formed aggregated islands, while mass clones were more scattered and exhibited higher migration capacity. Among several focal adhesion machinery proteins examined, only the expression and phosphorylation level of focal adhesion kinase (FAK) in mass clones was higher than in cyst clones, while other proteins showed no obvious differences. However, overexpression of wild type FAK in CA6 cells did not facilitate branching tubule formation in 0.1% collagen gel. Targeted decrease in the expression level of FAK in M610 cells with the application of antisense cDNA resulted in a marked reduction of branching tubule formation in 0.1% collagen gel and showed a down-regulation of fibronectin assembly, which is known to promote tubulogenesis. In contrast, overexpression of wild type FAK in CA6 cells had no effect on fibronectin assembly. Taken together, our data demonstrates that FAK is required, but not sufficient for HGF-independent branching tubulogenesis in MDCK cells