One-Dimensional Fermions and Bosonization

Pier Paolo Delsanto, G. Kaniadakis, M. And Scalerandi

B. G. Wybourne

Abstract The symmetry properties of bosons and fermions in a one‐dimensional harmonic oscillator are explored. It is shown that there is a one‐to‐one correspondence between the counts of the maximal spin states states formed by N‐noninteracting bosons and fermions in a one‐dimensional harmonic oscillator. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

A. V. Kulikov

Takehiko Mori, S Ikeda

One-dimensional Bose-Fermi mixture systems in a random potential are numerically investigated with focus on their superfluidity and localization properties. It is known that one-dimensional bosons and fermions behave differently in a weak random potential: Interacting bosons in a weak random potential exhibit superfluidity if the interactions are repulsive and not too strong, while interacting fermions with repulsive forces are localized in the presence of randomness. So the question is what happens if weakly interacting bosons and fermions are mixed in a random potential, which might be actually realized by the technique of trapping atoms on a random optical lattice. To answer this question we performed quantum Monte Carlo simulations of bosons and fermions on a one-dimensional lattice with random site energies. The result showed that when the boson-fermion interactions were attractive, both bosons and fermions tended to be localized. However when the boson- fermion interactions were repulsive and relatively weak, the superfluidity of bosons was enhanced and the fermions were delocalized.

Peter Kopietz

Yousuke Takeuchi, 弘之 森

Mixing-demixing transition in one-dimensional mixtures of fermions and bosons is numerically investigated by changing various parameters such as number densities of each component, fermion-boson interactions, boson-boson interactions, and hopping energies. In most cases we found clear evidence of the mixing-demixing transitions and identified the roles of each microscopic parameter in the transitions. Several phase diagrams were obtained.