We present results of numerically exact simulations of the Bose one-component plasma, i.e., a Bose gas with pairwise Coulomb interactions among particles and a uniform neutralizing background. We compute the superconducting transition temperature for a wide range of densities, in two and three dimensions, for both continuous and lattice versions of the model. The Coulomb potential causes the weakly interacting limit to be approached at high density, but gives rise to no qualitatively different behavior, vis-à-vis the superfluid transition, with respect to short-ranged interactions. Our results are of direct relevance to quantitative studies of bipolaron mechanisms of (high-temperature) superconductivity.
Quantum Monte Carlo simulations are used to investigate the two-dimensional superfluid properties of the hard-core boson model, which show a strong dependence on particle density and disorder. We obtain further evidence that a half-filled clean system becomes superfluid via a finite-temperature Kosterlitz-Thouless transition. The relationship between low-temperature superfluid density and particle density is symmetric and appears parabolic about the half filling point. Disorder appears to break the superfluid phase up into two distinct localized states, depending on the particle density. We find that these results strongly correlate with the results of several experiments on high-
Tc superconductors.
We study the ground-state properties of repulsively interacting bosons on the honeycomb lattice using large-scale quantum Monte Carlo simulations. In the hard-core limit, the half-filled system develops long-ranged diagonal order for sufficiently strong nearest-neighbor repulsion. This staggered solid melts at a first-order quantum phase transition into the superfluid phase, without the presence of any intermediate supersolid phase. Within the superfluid phase, both the superfluid density and the compressibility exhibit local minima near the particle (hole) density of one quarter, while the density and the condensate fraction show inflection points in this region. Relaxing the hard-core constraint, supersolid phases emerge for soft-core bosons. The suppression of the superfluid density is found to persist for sufficiently large, finite on-site repulsion.
The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension
dc which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on
4He absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.
A new approach developed in Ref.1 for investigating the spatial boson correlations at low temperatures is considered in the particular case of the Coulomb interaction potential. This approach is based on integro–differential equations for the radial distribution function and can be used beyond the weak coupling regime. PACS: 05.30.Jp, 67.90.+z Description of the charged Bose liquid, or, in other words, of the strongly correlated many–boson system with the Coulomb interparticle potential, is a long–standing problem of the condensed matter physics. Recently, interest in this problem has been renewed in the connection with the noteworthy results of applying the Bose and Bose–Fermi liquid models [2] to the explanation of various phenomena inherent in the superconductors with high critical temperatures. These models are based on the Bogoliubov approach [3] implying the weak coupling regime. For the system of charged bosons the weak coupling approximation can be used at small values of the Brueckner parameter rS ∼ 0.1. However, questions requiring detailed investigations often concern the materials with relatively low densities of charge carriers which correspond to rS−values even larger than those of the electron gas at 1 the metallic densities. For example, there are the results [4] testifying to the possibility of forming the so–called large bipolaron (e.g. the two–electron cluster with a large radius of electron–electron separation, see papers in Ref. [5]) inside the polaron environment at the electron densities ∼ 10 19 cm −3 close to the carrier densities of the heavily doped degenerate polar semiconductors. To investigate the possible phase transition of the charge carrier system from the polaron state to the bipolaron phase at these densities, one should operate with the charged Bose liquid of large bipolarons for rS ≫ 1. Indeed, the ”large–bipolaron“ Bohr radius can be expressed [4] as abip =
We present a strong-coupling expansion of the Bose-Hubbard model based on a mean-field treatment of the hopping term, while onsite fluctuations are taken into account exactly. This random phase approximation describes the universal features of the generic Mott-insulator--superfluid transition (induced by a density change) and the superfluid state near the phase transition. The critical quasiparticles at the quantum critical point have a quadratic dispersion with an effective mass
m∗ and their mutual interaction is described by an effective
s-wave scattering length
a∗. The singular part of the pressure takes the same form as in a dilute Bose gas, provided we replace the boson mass
m and the scattering length in vacuum
a by
m∗ and
a∗, and the density
n by the excess density $|n\ensuremath{-}{n}_{\mathrm{MI}}|$ of particles (or holes) with respect to the Mott insulator. We define a universal two-body contact
Cuniv that controls the high-momentum tail $\ensuremath{\sim}1/{|\mathbf{k}|}^{4}$ of the singular part
nksing of the momentum distribution. We also apply the strong-coupling RPA to a lattice model of hard-core bosons and find that the high-momentum distribution is controlled by a universal contact, in complete agreement with the Bose-Hubbard model. Finally, we discuss a continuum model of bosons in an optical lattice and define two additional two-body contacts: a short-distance universal contact
Cunivsd which controls the high-momentum tail of
nksing at scales larger than the inverse lattice spacing, and a full contact
C, which controls the high-momentum tail of the full-momentum distribution
nk.