Trap Effects in the Hubbard Model

Systems of interacting fermions in optical lattices, confined by a trapping interaction, can be described using the Hubbard Model in the Local Density Approximation (LDA). In the present work, we study the corrections to the LDA results, focusing in particular on analyzing their leading dependence on the trap size. We also study the scaling dependence on the trap size of the density and the density correlations in the limit of large trap size at fixed particle number, using the Trap Size Scaling (TSS) formalism

Universal quantum behaviors of interacting fermions in 1D traps: from few particles to the trap thermodynamic limit

We investigate the ground-state properties of trapped fermion systems described by the Hubbard model with an external confining potential. We discuss the universal behaviors of systems in different regimes: from few particles, i.e. in dilute regime, to the trap thermodynamic limit. The asymptotic trap-size (TS) dependence in the dilute regime (increasing the trap size l keeping the particle number N fixed) is described by a universal TS scaling controlled by the dilute fixed point associated with the metal-to-vacuum quantum transition. This scaling behavior is numerically checked by DMRG simulations of the one-dimensional (1D) Hubbard model. In particular, the particle density and its correlations show crossovers among different regimes: for strongly repulsive interactions they approach those of a spinless Fermi gas, for weak interactions those of a free Fermi gas, and for strongly attractive interactions they match those of a gas of hard-core bosonic molecules. The large-N behavior of systems at fixed N/l corresponds to a 1D trap thermodynamic limit. We address issues related to the accuracy of the local density approximation (LDA). We show that the particle density approaches its LDA in the large-l limit. When the trapped system is in the metallic phase, corrections at finite l are O(l^{-1}) and oscillating around the center of the trap. They become significantly larger at the boundary of the fermion cloud, where they get suppressed as O(l^{-1/3}) only. This anomalous behavior arises from the nontrivial scaling at the metal-to-vacuum transition occurring at the boundaries of the fermion cloud.Comment: 20 page

Nonequilibrium scenarios in cluster-forming quantum lattice models

We investigate the out-of-equilibrium physics of monodisperse bosonic ensembles on a square lattice. The effective Hamiltonian description of these systems is given in terms of an extended Hubbard model with cluster-forming interactions relevant to experimental realizations with cold Rydberg-dressed atoms. The ground state of the model, recently investigated in Phys. Rev. Lett. 123, 045301 (2019), features, aside from a superfluid and a stripe crystalline phase occurring at small and large interaction strength $V$, respectively, a rare first-order transition between an isotropic and an anisotropic stripe supersolid at intermediate $V$. By means of quantum Monte Carlo calculations we show that the equilibrium crystal may be turned into a glass by simulated temperature quenches and that out-of-equilibrium isotropic (super)solid states may emerge also when their equilibrium counterparts are anisotropic. These out-of-equilibrium states are of experimental interest, their excess energy with respect to the ground state being within the energy window typically accessed in cold atom experiments. We find, after quenching, no evidence of coexistence between superfluid and glassy behavior. Such an absence of superglassiness is qualitatively explained.Comment: 8 pages, 6 figure

Quasicrystalline Bose glass in the absence of (quasi)disorder

We study the low-temperature phases of interacting bosons on a two-dimensional quasicrystalline lattice. By means of numerically exact Path Integral Monte Carlo simulations, we show that for sufficiently weak interactions the system is a homogeneous Bose-Einstein condensate, which develops density modulations for increasing filling factor. The simultaneous occurrence of sizeable condensate fraction and density modulation can be interpreted as the analogous, in a quasicrystalline lattice, of supersolid phases occurring in conventional periodic lattices. For sufficiently large interaction strength and particle density, global condensation is lost and quantum exchanges are restricted to specific spatial regions. The emerging quantum phase is therefore a Bose Glass, which here is stabilized in the absence of any source of disorder or quasidisorder, purely as a result of the interplay between quantum effects and quasicrystalline substrate. This finding clearly indicates that (quasi)disorder is not essential to observe Bose Glass physics. Our results are of interest for ongoing experiments on (quasi)disorder-free quasicrystalline lattices.Comment: 5 pages, 4 figure

Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models

We investigate a model of hard-core bosons with infinitely repulsive nearest- and next-nearest-neighbor interactions in one dimension, introduced by Fendley, Sengupta and Sachdev in Phys. Rev. B 69, 075106 (2004). Using a combination of exact diagonalization, tensor network, and quantum Monte Carlo simulations, we show how an intermediate incommensurate phase separates a crystalline and a disordered phase. We base our analysis on a variety of diagnostics, including entanglement measures, fidelity susceptibility, correlation functions, and spectral properties. According to theoretical expectations, the disordered-to-incommensurate-phase transition point is compatible with Berezinskii-Kosterlitz-Thouless universal behaviour. The second transition is instead non-relativistic, with dynamical critical exponent $z > 1$. For the sake of comparison, we illustrate how some of the techniques applied here work at the Potts critical point present in the phase diagram of the model for finite next-nearest-neighbor repulsion. This latter application also allows to quantitatively estimate which system sizes are needed to match the conformal field theory spectra with experiments performing level spectroscopy.Comment: 18 pages, 14 figure

Finite-temperature critical behavior of long-range quantum Ising models

We study the phase diagram and critical properties of quantum Ising chains with long-range ferromagnetic interactions decaying in a power-law fashion with exponent $\alpha$, in regimes of direct interest for current trapped ion experiments. Using large-scale path integral Monte Carlo simulations, we investigate both the ground-state and the nonzero-temperature regimes. We identify the phase boundary of the ferromagnetic phase and obtain accurate estimates for the ferromagnetic-paramagnetic transition temperatures. We further determine the critical exponents of the respective transitions. Our results are in agreement with existing predictions for interaction exponents $\alpha > 1$ up to small deviations in some critical exponents. We also address the elusive regime $\alpha < 1$, where we find that the universality class of both the ground-state and nonzero-temperature transition is consistent with the mean-field limit at $\alpha = 0$. Our work not only contributes to the understanding of the equilibrium properties of long-range interacting quantum Ising models, but can also be important for addressing fundamental dynamical aspects, such as issues concerning the open question of thermalization in such models.Comment: 19 pages, 6 figures, updated to follow minor revisions suggested by the referee

14 MeV neutrons for 99Mo/99mTc production: Experiments, simulations and perspectives

Background: the gamma-emitting radionuclide Technetium-99m (99mTc) is still the workhorse of Single Photon Emission Computed Tomography (SPECT) as it is used worldwide for the diagnosis of a variety of phatological conditions.99mTc is obtained from99Mo/99mTc generators as pertechnetate ion, which is the ubiquitous starting material for the preparation of99mTc radiopharmaceuticals.99Mo in such generators is currently produced in nuclear fission reactors as a by-product of235U fission. Here we investigated an alternative route for the production of99Mo by irradiating a natural metallic molybdenum powder using a 14-MeV accelerator-driven neutron source. Methods: after irradiation, an efficient isolation and purification of the final99mTc-pertechnetate was carried out by means of solvent extraction. Monte Carlo simulations allowed reliable predictions of99Mo production rates for a newly designed 14-MeV neutron source (New Sorgentina Fusion Source). Results: in traceable metrological conditions, a level of radionuclidic purity consistent with accepted pharmaceutical quality standards, was achieved. Conclusions: we showed that this source, featuring a nominal neutron emission rate of about 1015s−1, may potentially supply an appreciable fraction of the current99Mo global demand. This study highlights that a robust and viable solution, alternative to nuclear fission reactors, can be accomplished to secure the long-term supply of99Mo

Concentration, pH, and Surface Charge Effects on Cadmium and Lead Sorption in Three Tropical Soils

Reactions of heavy metals with soil are important in determining metal fates in the environment. Sorption characteristics of two heavy metals, Cd and Pb, in three tropical soils (Mollisol, Oxisol, and Ultisol) from Puerto Rico were assessed at varying metal concentrations (0 to 1.2 mM) and pH values (approximately 2 to 7). All soils sorbed more Pb than Cd. Sorption maxima were obtained for each metal for the Oxisol and Ultisol soils, but not the Mollisol. Sorption appeared to depend more on soil mineralogy than organic matter content. Sorption isotherms were linear within the sorption envelope with similar slopes for each soil-metal curve, when plotting metal sorption as a function of pH. Cadmium and Pb isotherms yielded average slopes of approximately 36+/-1 and 28+/-1 units (percent increase in metal sorption per 1-unit increase in pH), respectively. Metal sorption depended more on metal type than soil composition. Cadmium sorption displayed a greater pH dependence than Pb. Cadmium sorption was less than or equal to the amount of negative surface charge except at pH values greater than the point of zero net charge (PZNC). This suggests that Cd was probably sorbed via electrostatic surface reactions and/or possible inner-sphere complexation at pH \u3e 3.7. However, the amount of Pb sorbed by the Oxisol was greater than the amount of negative surface charge, suggesting that Pb participates in inner-sphere surface reactions. Lead was sorbed more strongly than Cd in our soils and poses less of a threat to underlying ground water systems due to its lower mobility and availability

Concentrations of potentially toxic elements and soil environmental quality evaluation of a typical Prosecco vineyard of the Veneto region (NE Italy)

Purpose The aim of this work was to assess the concentrations of potentially toxic elements and to evaluate the soil quality of a typical Prosecco Denomination of Controlled and Guaranteed Origin vineyard of the Veneto region, NE Italy. Materials and methods Soil samples and leaves of Taraxacum officinale and Vitis vinifera were collected during spring–summer 2014. Element determination (Al, Cd, Cr, Cu, Fe, Mg, Mn, Ni, P, Pb, V, and Zn) were performed with ICP-OES after microwave digestion of samples. Soil quality was assessed via the biological soil quality (BSQ-ar) index. Lipid peroxidation test was performed to evaluate the vegetation oxidative stress, based on malondialdehyde (MDA) content via spectrophotometer. Results and discussion High concentrations of Al,Mg, and P were identified in soil, while high contents of Al, Cu, Fe, and Zn were found in V. vinifera leaves. The high concentrations in soil are probably due to agricultural activities, whereas those in leaves are probably due to atmospheric deposition and repeated use of foliar sprays in viticulture. The bioconcentration factor showed an effective transport of Cu, P, and Zn, from soil to leaf. The BSQ-ar values registered were similar to those obtained in preserved soils; hence, the biological class (VI) of these soils is high. The MDA content in T. officinale and V. vinifera leaves was below the reference value for T. officinale (2.9 ± 0.2 μM), suggesting that the metal content did not stress the vegetation in the investigated site. Conclusions The MDA value for V. vinifera (1.1 ± 0.7 μM) could be adopted as another control value for soil quality, which in our case is of Bgood quality.^ Moreover, our results suggest that high concentrations of elements detected in the analyzed samples do not influence negatively the quality of soil, but a better agronomic management could improve soil quality in the studied area