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Physical Review A

States of one-dimensional fermion clusters with repulsive interactions in optical lattices

M. C. Gordillo

Published Sep 25, 2017• 3 citations
Publisher

Abstract

We study the different states (metal, Mott insulator, and band insulator) appearing in clusters of fermions confined in one-dimensional optical lattices. To describe these systems, instead of the standard Hubbard Hamiltonian, a continuous model with repulsive contact interactions between unlike-spin particles is used. The corresponding Schr\"odinger equations are solved using a diffusion Monte Carlo algorithm. We consider both balanced (same number of spin-up and spin-down fermions) and unbalanced arrangements with the same number of atoms in the minority component ($N\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}5$). We find that the structure of the clusters in both the weak- and the strong-coupling limits can be predicted to some extent from the solutions of the noninteracting Schr\"odinger equations describing the same systems, in line with findings in the previous literature.

DOI
10.1103/physreva.96.033630

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We study the different states (metal, Mott insulator, and band insulator) appearing in clusters of fermions confined in one-dimensional optical lattices. To describe these systems, instead of the standard Hubbard Hamiltonian, a continuous model with repulsive contact interactions between unlike-spin particles is used. The corresponding Schr"odinger equations are solved using a diffusion Monte Carlo algorithm. We consider both balanced (same number of spin-up and spin-down fermions) and unbalanced arrangements with the same number of atoms in the minority component (N=5N\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}5N=5). We find that the structure of the clusters in both the weak- and the strong-coupling limits can be predicted to some extent from the solutions of the noninteracting Schr"odinger equations describing the same systems, in line with findings in the previous literature.
Abstract We studied the behavior of mixtures of 173Yb (with symmetry up to SU(6)) and 171Yb (up to SU(2)) fermionic isotopes loaded in one-dimensional (1D) optical lattices. To do so, we solved the Schrödinger equation describing different systems using a diffusion Monte Carlo technique. We considered continuous Hamiltonians in which the interactions between atoms of different species (isotopes and/or spins) were modeled by contact potentials with parameters derived from their experimental scattering lengths. This implies that we can find both attractive and repulsive interactions between fermion pairs in the same cluster. The strength of those interactions can be changed by varying the transverse confinement, leading to different cluster behaviors. Only balanced clusters, i.e. with the same number of 173Yb and 171Yb atoms were considered. We found that the standard state for these clusters is a metallic-like one with different populations of 173Yb–171Yb molecule-like pairs in each optical lattice potential well. However, for big enough clusters, insulator-like states are also possible.
The behavior of small clusters of one spin-up and two spin-down fermions with unlike-spin repulsive interactions in one-dimensional optical lattices was calculated using a diffusion Monte Carlo technique. We considered also a harmonic potential in the longitudinal direction to make our system resemble the standard experimental setups. When the interparticle repulsion is strong enough, the onset of fermionization is observed irrespective of the optical lattice parameters considered, in line with previous results for pure harmonic confinement. However, fermionization can also be seen even for small interparticle couplings if the optical potential is deep enough. In addition, for certain values of the wavelengths and the potential depths defining the lattice, Mott insulators in the fermionization limit with only three atoms were found.
Abstract We describe the possible states of four-fermion clusters loaded in one-dimensional optical lattices with an additional harmonic confinement when the interactions between particles of different spin are contact-like. We have found that, depending on the depth of the potential well, the wavelength of the laser, and the strength of the repulsive interactions, we can have ground states that have unpaired spins (paramagnetic), all the spins paired (diamagnetic) or a degenerate mixture of different configurations. In this last case, the cluster could be either a metal or a Mott insulator. The characteristics of the ground state can be inferred to some extent from the solutions of non-interacting Schrödinger equations for the same arrangements.
Abstract The behaviour of fermion clusters with SU(N) symmetry loaded in one-dimensional optical lattices and described by continuous Hamiltonians was studied using a diffusion Monte Carlo (DMC) technique. The state diagrams of SU(6) and SU(2) arrangements with the same number of particles were calculated and found virtually identical. The only difference was the absence of a band insulator in the SU(N) case in the range of optical lattice depths considered (V 0 = 0–12 E R ; E R , recoil energy of the lattice) in the non-interacting limit for N > 2. The appearance of that state was signalled by a noticeable change in the shape of the momentum distributions in going from a metal to a band insulator.
By using a diffusion Monte Carlo (DMC) technique, we studied the behaviour of a mixture of spin-up and spin-down cold fermionic atoms confined in one-dimensional harmonic potentials. We considered only small balanced clusters (up to eight atoms) or arrangements in which the difference between the population of fermions with different spins is one (with a maximum total number of nine). The atom–atom interactions were modeled by a contact repulsive potential. We focused on the ordering of the confined fermions, finding that the probability of having a pure antiferromagnetic arrangement of atoms decreases strongly with the number of fermions, as to be almost negligible for our largest clusters. Exactly the same can be said of a pure ferromagnetic state.
We present an extensive numerical study of the ground-state properties of confined repulsively interacting fermions in one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe ansatz based local-density approximation for the correlation energy that accounts for Luttinger-liquid and Mott-insulator physics. Semianalytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-type local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these provide a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.