Universal quantum behavior of interacting fermions in onedimensional traps: From few particles to the trap thermodynamic limit
Abstract
We investigate the groundstate properties of trapped fermion systems described by the Hubbard model with an external confining potential. We discuss the universal behaviors of systems in different regimes: from few particles, i.e., in dilute regimes, to the trap thermodynamic limit. The asymptotic trapsize (TS) dependence in the dilute regime (increasing the trap size ℓ keeping the particle number N fixed) is described by a universal TS scaling controlled by the dilute fixed point associated with the metaltovacuum quantum transition. This scaling behavior is numerically checked by DMRG simulations of the onedimensional (1D) Hubbard model. In particular, the particle density and its correlations show crossovers among different regimes: for strongly repulsive interactions they approach those of a spinless Fermi gas, for weak interactions those of a free Fermi gas, and for strongly attractive interactions they match those of a gas of hardcore bosonic molecules. The largeN limit keeping the ratio N /ℓ fixed corresponds to a 1D trap thermodynamic limit. We address issues related to the accuracy of the local density approximation (LDA). We show that the particle density approaches its LDA in the largeℓ limit. When the trapped system is in the metallic phase, corrections at finite ℓ are O (ℓ^{1}) and oscillating around the center of the trap. They become significantly larger at the boundary of the fermion cloud, where they get suppressed as O (ℓ^{1/3}) only. This anomalous behavior arises from the nontrivial scaling at the metaltovacuum transition occurring at the boundaries of the fermion cloud.
 Publication:

Physical Review A
 Pub Date:
 February 2014
 DOI:
 10.1103/PhysRevA.89.023635
 arXiv:
 arXiv:1401.3514
 Bibcode:
 2014PhRvA..89b3635A
 Keywords:

 03.75.Ss;
 71.10.Fd;
 05.30.Fk;
 05.10.Cc;
 Degenerate Fermi gases;
 Lattice fermion models;
 Fermion systems and electron gas;
 Renormalization group methods;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Statistical Mechanics
 EPrint:
 20 pages