Spin and charge velocities of one-dimensional boson-fermion mixture

陽介 竹内

E. Orignac, Masahisa Tsuchiizu, Yoshikazu Suzumura

We study a mixture of one-dimensional bosons and spinless fermions at incommensurate filling using phenomenological bosonization and Green's function techniques. We derive the relation between the parameters of the microscopic Hamiltonian and macroscopic observables. Galilean invariance results in extra constraints for the current-current interactions. We obtain the exact exponents for the various response functions, and show that superfluid fluctuations are enhanced by the effective boson-fermion density-density interaction and suppressed by the effective boson-fermion current-current interaction. In the case of a bosonized model with purely density-density interaction, when the effective boson-fermion density-density interaction is weak enough, the superfluid exponent of the bosons has a nonmonotonic variation with the ratio of the fermion velocity to the boson velocity. In contrast, the density-wave exponent and the exponent for fermionic superfluidity are monotonic functions of the velocity ratio.

Pinaki Sengupta, Leonid P. Pryadko

We study numerically and analytically the phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional lattice. In particular, along a symmetry plane in the parameter space, we obtain the exact boundary of the boson-demixing transition from the Bethe ansatz solution of the standard Hubbard model. For a region of parameter space, we prove the existence of boson-fermion mixed phase at all densities. This phase is a two-component Luttinger liquid for weak couplings or for incommensurate total density, otherwise it has a charge gap but retains a gapless mode of mixture composition fluctuations. We show that the static density correlations in these two regimes are markedly different.

M. E. Ta gin, A. I., Mehmet Özgür Oktel +1 more

Yoshio Kuramoto

Pinaki Sengupta, Leonid P. Pryadko

We study numerically and analytically the phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional lattice. In particular, along a symmetry plane in the parameter space, we obtain the exact boundary of the boson-demixing transition from the Bethe ansatz solution of the standard Hubbard model. For a region of parameter space, we prove the existence of boson-fermion mixed phase at all densities. This phase is a two-component Luttinger liquid for weak couplings or for incommensurate total density, otherwise it has a charge gap but retains a gapless mode of mixture composition fluctuations. We show that the static density correlations in these two regimes are markedly different.