The excitation spectrum of the frustrated spin-$1/2$ Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted whic
h yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at $J_2=0.25J_1$ and an onset of incommensurability in the dispersion relation at $J_2=9/17J_1$ [as in S. Brehmer emph{et al.}, J. Phys.: Condens. Matter textbf{10}, 1103 (1998)]. These analytical results provide a good support for the understanding of exact diagonalization spectra, assuming an independent spinons picture.
The magnetic responses of a spin-1/2 ladder doped with non-magnetic impurities are studied using various methods and including the regime where frustration induces incommensurability. Several improvements are made on the results of the seminal work o
f Sigrist and Furusaki [J. Phys. Soc. Jpn. 65, 2385 (1996)]. Deviations from the Brillouin magnetic curve due to interactions are also analyzed. First, the magnetic profile around a single impurity and effective interactions between impurities are analyzed within the bond-operator mean-field theory and compared to density-matrix renormalization group calculations. Then, the temperature behavior of the Curie constant is studied in details. At zero-temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattice and compute exactly the distribution of ladder cluster due to chain breaking effects. Using exact diagonalization and quantum Monte-Carlo methods on the effective model, the temperature dependence of the Curie constant is compared to a random dimer model and a real-space renormalization group scenario. Next, the low-part of the magnetic curve corresponding to the contribution of impurities is computed using exact diagonalization. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from the Brillouin response. At zero-temperature, the effective model prediction agrees relatively well with density-matrix renormalization group calculations. Finite-temperature effects are displayed within the effective model and for large depleted ladder models using quantum Monte-Carlo simulations. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu2PO6 compound and other spin-gapped materials are briefly discussed.
The quantum evolution of a cloud of bosons initially localized on part of a one dimensional optical lattice and suddenly subjected to a linear ramp is studied, realizing a quantum analog of the Galileo ramp experiment. The main remarkable effects of
this realistic setup are revealed using analytical and numerical methods. Only part of the particles are ejected for a high enough ramp, while the others remain self-trapped. Then, the trapped density profile displays rich dynamics with Josephson-like oscillations around a plateau. This setup, by coupling bound states to propagative modes, creates two diverging condensates for which the entanglement is computed and related to the equilibrium one. Further, we address the role of integrability on the entanglement and on the damping and thermalization of simple observables.
We consider two-component one-dimensional quantum gases at special imbalanced commensurabilities which lead to the formation of multimer (multi-particle bound-states) as the dominant order parameter. Luttinger liquid theory supports a mode-locking me
chanism in which mass (or velocity) asymmetry is identified as the key ingredient to stabilize such states. While the scenario is valid both in the continuum and on a lattice, the effects of umklapp terms relevant for densities commensurate with the lattice spacing are also mentioned. These ideas are illustrated and confronted with the physics of the asymmetric (mass-imbalanced) fermionic Hubbard model with attractive interactions and densities such that a trimer phase can be stabilized. Phase diagrams are computed using density-matrix renormalization group techniques, showing the important role of the total density in achieving the novel phase. The effective physics of the trimer gas is as well studied. Lastly, the effect of a parabolic confinement and the emergence of a crystal phase of trimers are briefly addressed. This model has connections with the physics of imbalanced two-component fermionic gases and Bose-Fermi mixtures as the latter gives a good phenomenological description of the numerics in the strong-coupling regime.
Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the ratio of
adjacent level spacings, useful at large interaction, to distinguish between chaotic and non-chaotic regimes. After revisiting the bare Bose-Hubbard model, we study the effect of two different perturbations: next-nearest neighbor hopping and nearest-neighbor interaction. The system size dependence is investigated together with the effect of the proximity to integrable points or lines. Lastly, we discuss the consequences of a cutoff in the number of onsite bosons onto the level statistics.
