Fermions and Bosons at Low Temperature

Ronald D. Blatherwick

Kyoko Shirasaki, Eiji Nakano, Hiroyuki Yabu

We investigate the mechanical instability toward density collapse and the transition temperature of Bose-Einstein condensation (BEC) in the weakly coupled boson-fermion many-body mixture of single-component boson and fermion gases, in the case of the repulsive boson-boson and attractive boson-fermion interactions; no fermion-fermion interaction is assumed to be originated from the Pauli exclusion because of the diluteness of the mixture. The mechanical instability occurs in the bosonic gas where the induced boson-boson attraction mediated by the fermion polarization overcomes the boson-boson repulsive interaction at low temperatures. We calculate the onset temperature of the mechanical instability and the BEC transition temperature for the interaction strength and the boson-fermion number ratio. We also discuss the relation between the mechanical instability and the BEC transition using a diagrammatic method.

Arnout Jozef Ceulemans

Hagen M. Kleinert, She-Sheng Xue

Our goal is to understand the phenomena arising in optical lattice fermions at low temperature in an external magnetic field. Varying the field, the attraction between any two fermions can be made arbitrarily strong, where composite bosons form via so-called Feshbach resonances. By setting up strong-coupling equations for fermions, we find that in spatial dimension d>2 they couple to bosons which dress up fermions and lead to new massive composite fermions. At low enough temperature, we obtain the critical temperature at which composite bosons undergo the Bose–Einstein condensate (BEC), leading to BEC-dressing massive fermions. These form tightly bound pair states which are new bosonic quasi-particles producing a BEC-type condensate. A quantum critical point is found and the formation of condensates of complex quasi-particles is speculated over.

Jun-ichi Igarashi, Peter Fulde

Motion of a single hole is studied at finite temperatures in the t-J model on a slave-fermion Schwinger-boson representation. The spin fluctuation is treated with the mean-field theory of Arovas and Auerbach. The Green's function for the slave fermion is calculated within the self-consistent Born approximation. A sharp quasiparticle peak is found to be separated from a broad spectrum of incoherence in the spectral function for low temperatures. The Green's function for the physical hole is calculated by taking account of the multiple scattering between the slave fermion and the Schwinger boson. A bound state of the slave fermion and the Schwinger boson is found at low temperatures, suggesting that the spin and the charge cannot be separated into a simple form. The energy of the bound state is minimized at momenta (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2, \ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2), indicating that a small pocketlike Fermi surface is formed around the momenta for low concentrations of dopant holes.