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arXiv:1410.1034 · Physical Review A

Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

Julia Stasińska, Mateusz Łącki, Omjyoti Dutta, Jakub Zakrzewski, Maciej Lewenstein

Published Dec 24, 2014• 4 citations
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Abstract

We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the site-dependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the model with chemical-potential disorder. These triple points, however, cease to exist after the addition of the hopping disorder.

DOI
10.1103/physreva.90.063634

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We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the site-dependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the model with chemical-potential disorder. These triple points, however, cease to exist after the addition of the hopping disorder.
Recently it has been suggested that fermions whose hopping amplitude is quenched to extremely low values provide a convenient source of local disorder for lattice bosonic systems realized in current experiment on ultracold atoms. Here we investigate the phase diagram of such systems, which provide the experimental realization of a Bose-Hubbard model whose local potentials are randomly extracted from a binary distribution. Adopting a site-dependent Gutzwiller description of the state of the system, we address one- and two-dimensional lattices and obtain results agreeing with previous findings, as far as the compressibility of the system is concerned. We discuss the expected peaks in the experimental excitation spectrum of the system, related to the incompressible phases, and the superfluid character of the partially compressible regions characterizing the phase diagram of systems with binary disorder. In our investigation we make use of several analytical results whose derivation is described in appendixes, and whose validity is not limited to the system under concern.
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Experimental realizations of disorder in optical lattices generate a distribution of the Bose-Hubbard (BH) parameters, like on-site potentials, hopping strengths, and interaction energies. We analyze this distribution for bosons in a two-dimensional bichromatic quasiperiodic potential by determining the generalized Wannier functions and calculating the corresponding BH parameters. Using a local mean-field cluster analysis, we study the effect of the corresponding disorder on the phase diagrams. We find a substantial amount of disorder in the hopping strengths, which produces strong deviations from the phase diagram of the disordered BH model with purely random on-site potentials.
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The phase transitions in the Bose-Fermi-Hubbard model are investigated.The boson Green's function is calculated in the random phase approximation (RPA) and the formalism of the Hubbard operators is used.The regions of existence of the superfluid and Mott insulator phases are established and the (µ, t) (the boson chemical potential vs. hopping parameter) phase diagrams are built at different values of boson-fermion interaction constant (in the regimes of fixed chemical potential or fixed concentration of fermions).The effect of temperature change on this transition is analyzed and the phase diagrams in the (T, µ) plane are constructed.The role of thermal activation of the ion hopping is investigated by taking into account the temperature dependence of the transfer parameter.The reconstruction of the Mott-insulator lobes due to this effect is analyzed.
Both mixtures of atomic Bose-Einstein condensates and systems with atoms trapped in optical lattices have been intensely explored theoretically, mainly due to the exceptional developments on the experimental side. We investigate the properties of ultracold atomic impurities (bosons) immersed in a vortex lattice of a second Bose-condensed species. In contrast to the static optical-lattice configuration, the vortex lattice presents intrinsic dynamics given by its Tkachenko modes. These excitations induce additional correlations between the impurities, which consist of a long-range attractive potential and a density-dependent hopping, described here in the framework of an extended Bose-Hubbard model. We compute the quantum phase diagram of the impurity species through a Gutzwiller ansatz and through the mean-field approach, and separately identify the effects of the two additional terms, i.e., the shift and the deformation of the Mott-insulator lobes. The long-range attraction, in particular, induces the existence of a triple point in the phase diagram, in agreement with previous quantum Monte Carlo calculations [Chaviguri et al., Phys. Rev. A 95, 053639 (2017)].