Universal quantum behavior of interacting fermions in one-dimensional traps: From few particles to the trap thermodynamic limit

Dip. di Fisica dell’Universita di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy(Dated: January 16, 2014)We investigate the ground-state properties of trapped fermion systems described by the Hubbardmodel with an external confining potential. We discuss the universal behaviors of systems in differentregimes: from few particles, i.e. in dilute regime, to the trap thermodynamic limit.The asymptotic trap-size (TS) dependence in the dilute regime (increasing the trap size l keepingthe particle number N fixed) is described by a universal TS scaling controlled by the dilute fixedpoint associated with the metal-to-vacuum quantum transition. This scaling behavior is numericallychecked by DMRG simulations of the one-dimensional (1D) Hubbard model. In particular, theparticle density and its correlations show crossovers among different regimes: for strongly repulsiveinteractions they approach those of a spinless Fermi gas, for weak interactions those of a free Fermigas, and for strongly attractive interactions they match those of a gas of hard-core bosonic molecules.The large-N behavior of systems at fixed N/l corresponds to a 1D trap thermodynamic limit. Weaddress issues related to the accuracy of the local density approximation (LDA). We show that theparticle density approaches its LDA in the large-l limit. When the trapped system is in the metallicphase, corrections at finite l are O(l