Luttinger-liquid behavior of one-dimensional He-3

The ground-state properties of one-dimensional He-3 are studied using quantum Monte Carlo methods. The equation of state is calculated in a wide range of physically relevant densities and is well interpolated by a power-series fit. The Luttinger liquid theory is found to describe the long-range properties of the correlation functions. The density dependence of the Luttinger parameter is explicitly found, and interestingly it shows a nonmonotonic behavior. Depending on the density, the static structure factor can be a smooth function of the momentum or might contain a peak of a finite or infinite height. Although no phase transitions are present in the system, we identify a number of physically different regimes, including an ideal Fermi gas, aPostprint (published version

Phase diagram of quasi-two-dimensional bosons in a laser-speckle potential

We have studied the phase diagram of a quasi-two-dimensional interacting Bose gas at zero temperature in the presence of random potential created by laser speckles. The superfluid fraction and the fraction of particles with zero momentum are obtained within the mean-field Gross-Pitaevskii theory and in diffusion Monte Carlo simulations. We find a transition from the superfluid to the insulating state when the strength of the disorder grows. Estimations of the critical parameters are compared with the predictions of the percolation theory in the Thomas-Fermi approximation. Analytical expressions for the zero-momentum fraction and the superfluid fraction are derived in the limit of weak disorder and weak interactions within the framework of the Bogoliubov theory. Limits of validity of various approximations are discussed.Peer ReviewedPostprint (author's final draft

One-dimensional multicomponent Fermi gas in a trap: quantum Monte Carlo study

One-dimensional world is very unusual as there is an interplay between quantum statistics and geometry, and a strong short-range repulsion between atoms mimics Fermi exclusion principle, fermionizing the system. Instead, a system with a large number of components with a single atom in each, on the opposite acquires many bosonic properties. We study the ground-state properties a multi-component Fermi gas trapped in a harmonic trap by fixed-node diffusion Monte Carlo method. We investigate how the energetic properties (energy, contact) and correlation functions (density profile and momentum distribution) evolve as the number of components is changed. It is shown that the system fermionizes in the limit of strong interactions. Analytical expression are derived in the limit of weak interactions within the local density approximation for arbitrary number of components and for one plus one particle using an exact solution.Comment: 15 pages, 5 figure

Ultradilute low-dimensional liquids

We calculate the energy of one- and two-dimensional weakly interacting Bose-Bose mixtures analytically in the Bogoliubov approximation and by using the diffusion Monte Carlo technique. We show that in the case of attractive inter- and repulsive intraspecies interactions the energy per particle has a minimum at a finite density corresponding to a liquid state. We derive the Gross-Pitaevskii equation to describe droplets of such liquids and solve it analytically in the one-dimensional case.Comment: published version + supplemental materia

Phase diagram of a quantum Coulomb wire

We report the quantum phase diagram of a one-dimensional Coulomb wire obtained using the path integral Monte Carlo (PIMC) method. The exact knowledge of the nodal points of this system permits us to find the energy in an exact way, solving the sign problem which spoils fermionic calculations in higher dimensions. The results obtained allow for the determination of the stability domain, in terms of density and temperature, of the one-dimensional Wigner crystal. At low temperatures, the quantum wire reaches the quantum-degenerate regime, which is also described by the diffusion Monte Carlo method. Increasing the temperature the system transforms to a classical Boltzmann gas which we simulate using classical Monte Carlo. At large enough density, we identify a one-dimensional ideal Fermi gas which remains quantum up to higher temperatures than in two- and three-dimensional electron gases. The obtained phase diagram as well as the energetic and structural properties of this system are relevant to experiments with electrons in quantum wires and to Coulomb ions in one-dimensional confinement.Comment: 5 pages, 4 figure

Lieb's soliton-like excitations in harmonic trap

We study the solitonic Lieb II branch of excitations in one-dimensional Bose-gas in homogeneous and trapped geometry. Using Bethe-ansatz Lieb's equations we calculate the "effective number of atoms" and the "effective mass" of the excitation. The equations of motion of the excitation are defined by the ratio of these quantities. The frequency of oscillations of the excitation in a harmonic trap is calculated. It changes continuously from its "soliton-like" value \omega_h/\sqrt{2} in the high density mean field regime to \omega_h in the low density Tonks-Girardeau regime with \omega_h the frequency of the harmonic trapping. Particular attention is paid to the effective mass of a soliton with velocity near the speed of sound.Comment: 5 figure