The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases

We compute the phase diagram of the one-dimensional Bose-Hubbard model with a quasi-periodic potential by means of the density-matrix renormalization group technique. This model describes the physics of cold atoms loaded in an optical lattice in the presence of a superlattice potential whose wave length is incommensurate with the main lattice wave length. After discussing the conditions under which the model can be realized experimentally, the study of the density vs. the chemical potential curves for a non-trapped system unveils the existence of gapped phases at incommensurate densities interpreted as incommensurate charge-density wave phases. Furthermore, a localization transition is known to occur above a critical value of the potential depth V_2 in the case of free and hard-core bosons. We extend these results to soft-core bosons for which the phase diagrams at fixed densities display new features compared with the phase diagrams known for random box distribution disorder. In particular, a direct transition from the superfluid phase to the Mott insulating phase is found at finite V_2. Evidence for reentrances of the superfluid phase upon increasing interactions is presented. We finally comment on different ways to probe the emergent quantum phases and most importantly, the existence of a critical value for the localization transition. The later feature can be investigated by looking at the expansion of the cloud after releasing the trap.Comment: 19 pages, 20 figure

Haldane-gap chains in a magnetic field

We consider quasi one dimensional spin-1 Heisenberg chains with crystal field anisotropy in a uniform magnetic field. We determine the dynamical structure factor in various limits and obtain a fairly complete qualitative picture of how it changes with the applied field. In particular, we discuss how the width of the higher energy single magnon modes depends on the field. We consider the effects of a weak interchain coupling. We discuss the relevance of our results for recent neutron scattering experiments on the quasi-1D Haldane-gap compound NDMAP.Comment: 34 pages, 7 figure

Magnetization Plateaus in a Solvable 3-Leg Spin Ladder

We present a solvable ladder model which displays magnetization plateaus at fractional values of the total magnetization. Plateau signatures are also shown to exist along special lines. The model has isotropic Heisenberg interactions with additional many-body terms. The phase diagram can be calculated exactly for all values of the rung coupling and the magnetic field. We also derive the anomalous behaviour of the susceptibility near the plateau boundaries. There is good agreement with the phase diagram obtained recently for the pure Heisenberg ladders by numerical and perturbative techniques.Comment: 4 pages, revtex, 3 postscript figures, small changes to the text and references update

A Strong-Coupling Approach to the Magnetization Process of Polymerized Quantum Spin Chains

Polymerized quantum spin chains (i.e. spin chains with a periodic modulation of the coupling constants) exhibit plateaux in their magnetization curves when subjected to homogeneous external magnetic fields. We argue that the strong-coupling limit yields a simple but general explanation for the appearance of plateaux as well as of the associated quantization condition on the magnetization. We then proceed to explicitly compute series for the plateau boundaries of trimerized and quadrumerized spin-1/2 chains. The picture is completed by a discussion how the universality classes associated to the transitions at the boundaries of magnetization plateaux arise in many cases from a first order strong-coupling effective Hamiltonian.Comment: 5 pages REVTeX, three PostScript figures included using psfig.st

Random bond XXZ chains with modulated couplings

The magnetization behavior of q-periodic antiferromagnetic spin 1/2 Heisenberg chains under uniform magnetic fields is investigated in a background of disorder exchange distributions. By means of both real space decimation procedures and numerical diagonalizations in XX chains, it is found that for binary disorder the magnetization exhibits wide plateaux at values of 1+2(p-1)/q, where p is the disorder strength. In contrast, no spin gaps are observed in the presence of continuous exchange distributions. We also study the magnetic susceptibility at low magnetic fields. For odd q-modulations the susceptibility exhibits a universal singularity, whereas for q even it displays a non-universal power law behavior depending on the parameters of the distribution.Comment: 4 pages, 3 figures. Final version to appear in PR

Successive opening of the Fermi surface in doped N-leg Hubbard ladders

We study the effect of doping away from half-filling in weakly (but finitely) interacting N-leg Hubbard ladders using renormalization group and bosonization techniques. For a small on-site repulsion U, the N-leg Hubbard ladders are equivalent to a N-band model, where at half-filling the Fermi velocities are v_{1}=v_{N}<v_{2}=v_{N-1}<... We then obtain a hierarchy of energy-scales, where the band pairs (j,N+1-j) are successively frozen out. The low-energy Hamiltonian is then the sum of N/2 (or (N-1)/2 for N odd) two-leg ladder Hamiltonians without gapless excitations (plus a single chain for N odd with one gapless spin mode), similar to the N-leg Heisenberg spin-ladders. The energy-scales lead to a hierarchy of gaps. Upon doping away from half-filling, the holes enter first the band(s) with the smallest gap: For odd N, the holes enter first the nonbonding band (N+1)/2 and the phase is a Luttinger liquid, while for even N, the holes enter first the band pair (N/2,N/2+1) and the phase is a Luther-Emery liquid, similar to numerical treatments of the t-J model, i.e., at and close to half-filling, the phases of the Hubbard ladders for small and large U are the same. For increasing doping, hole-pairs subsequently enter at critical dopings the other band pairs (j,N+1-j) (accompanied by a diverging compressibility): The Fermi surface is successively opened by doping, starting near the wave vector (pi/2,pi/2). Explicit calculations are given for the cases N=3,4.Comment: 10 pages, 4 figures, to be published in Phys. Rev.

Metal-Kondo insulating transitions and transport in one dimension

We study two different metal-insulating transitions possibly occurring in one-dimensional Kondo lattices. First, we show how doping the pure Kondo lattice model in the strong-coupling limit, results in a Pokrovsky-Talapov transition. This produces a conducting state with a charge susceptibility diverging as the inverse of the doping, that seems in agreement with numerical datas. Second, in the weak-coupling region, Kondo insulating transitions arise due to the consequent renormalization of the backward Kondo scattering. Here, the interplay between Kondo effect and electron-electron interactions gives rise to significant phenomena in transport, in the high-temperature delocalized (ballistic) regime. For repulsive interactions, as a perfect signature of Kondo localization, the conductivity is found to decrease monotonically with temperature. When interactions become attractive, spin fluctuations in the electron (Luttinger-type) liquid are suddenly lowered. The latter is less localized by magnetic impurities than for the repulsive counterpart, and as a result a large jump in the Drude weight and a maximum in the conductivity arise in the entrance of the Kondo insulating phase. These can be viewed as remnants of s-wave superconductivity arising for attractive enough interactions. Comparisons with transport in the single impurity model are also performed. We finally discuss the case of randomly distributed magnetic defects, and the applications on persistent currents of mesoscopic rings.Comment: 21 pages, two columns, 5 figures and 1 table; Final version: To appear in Physical Review