No abstract

We study (by an exact numerical scheme) the single-particle density matrix of ∼ 10 3 ultracold atoms in an optical lattice with a parabolic confining potential. Our simulation is directly relevant to the interpretation and further development of the recent pioneering experiment [1]. In particular, we show that restructuring of the spatial distribution of the superfluid component when a domain of Mott-insulator phase appears in the system, results in a fine structure of the particle momentum distribution. This feature may be used to locate the point of the superfluid-Mott-insulator transition.The fascinating physics of the superfluid-insulator transition in a system of interacting bosons on a lattice has been attracting constant interest of theorists during recent years [2][3][4][5][6][7][8][9]. Lattice bosons is one of the simplest many-body problems with strong competition between the potential and kinetic energy, and a typical example of the quantum phase transition system. One of its great advantages is the possibility to study it by powerful Monte Carlo methods which nowadays allow simulations of many thousands of particles at low temperature with unprecedented accuracy (see, e.g., [9]). However, until very recently the canonical Bose-Hubbard model(where a † i creates a particle on the site i, < ij > stands for the nearest-neighbor sites, n i = a † i a i , and t, U , and µ i , are the hopping amplitude, the on-site interaction, and the on-site external field, respectively) was not particularly useful in the analysis of realistic systems. The situation has changed with the exciting success of the experiment by Greiner et al.[1] (originally proposed by Jaksch et al. [10]) in which a gas of ultracold 87 Rb atoms was trapped in a three-dimensional, simple-cubic optical lattice potential. The uniqueness of the new system is that it is adequately described by the Bose-Hubbard Hamiltonian [10,1], and allows virtually an unlimited control over the strength of the effective interparticle interaction U/t and particle density.The characteristic feature of the experimental setup of Ref.[1] is the presence of the overall parabolic potential V (r) which confines the sample. This feature could be of great advantage if one was able to directly measure the spatial density distribution in the trap. We recall the structure of the µ − U/t phase diagram for the BoseHubbard system [2] which predicts commensurate particle density distribution for the insulating phase whenever the chemical potential lies within the Mott-Hubbard gap. The slowly varying (at the length scale of the lattice period) trapping potential effectively provides a scan over µ of this phase diagram at a fixed value of U/t.Unfortunately, what is measured in the experiment is not the original spatial density distribution in the trap, but the absorption image of the free evolving atomic cloud, after the trapping/optical potential is removed; i.e. the quantity which is directly related to the the singleparticle density matrix in momentum space, ρ kk = n k .[This st...

We demonstrate that the ``worm'' algorithm allows very effective and precise quantum Monte Carlo (QMC) simulations of spin systems in a magnetic field, and its auto-correlation time is rather insensitive to the value of H at low temperature. Magnetization curves for the $s=1/2$ and $s=1$ chains are presented and compared with existing Bethe ansatz and exact diagonalization results. From the Green function analysis we deduce the magnon spectra in the s=1 system, and directly establish the "relativistic" form E(p)=(\Delta ^2 +v^2 p^2)^{1/2} of the dispersion law.Comment: 6 pages, 8 figures; removed discussion of spin-2 case - will be published later in a separate pape

No abstract

We consider topological supercurrent excitations (SC) in 1D mesoscopic rings.Under certain conditions such excitations are well-defined except for (i) a tunneling between resonating states with clockwise and anti-clockwise currents, which may be characterized by the amplitude ∆, and (ii) a decay of SC assisted by phonons of the substrate, both effects being macroscopically small.Our approach being based on the hydrodynamical action for the phase field and its generalization to the effective Hamiltonian explicitly takes into account transitions between the states with different topological numbers and turns out to be very effective for the calculation of ∆ and estimation of the decay width of SC, as well as for the unified description of all known 1D superfluid-insulator transitions.Most attention is paid to the calculation of the macroscopic scaling of ∆ (the main superfluid characteristic of a mesoscopic system) under different conditions: a commensurate system, a system with single impurity, and a disordered system. The results are in a very good agreement with the exactdiagonalization spectra of the boson Hubbard models.Apart from really 1D electron wires we discuss two other important experimental systems: the 2D electron gas in the FQHE state and quasi-1D