Long-range topological insulators and weakened bulk-boundary correspondence

We formalize the appearance of new types of insulators in long-range (LR) fermionic systems. These phases are not included in the "ten-fold way classification" (TWC) for the short-range (SR) topological insulators. This conclusion is obtained studying at first specific one-dimensional LR examples, in particular their phase diagrams and contents in symmetries and entanglement. The purely long-range phases (LRP) are signaled by the violation of the area-law for the Von Neumann entropy and by corresponding peculiar distributions for the entanglement spectrum (ES). The origin of the deviations from the TWC is analyzed from a more general point of view and in any dimension. In particular, it is found related with a particular type of divergences occurring in the spectrum, due to the LR couplings. A satisfying characterization for the LRP can be achieved at least for one-dimensional systems, as well as the connected definition of a nontrivial topology, provided a careful evaluation of the LR contributions. Our results lead to reconsider the definition of correlation length in LR systems. The same analysis also allows to infer, at least for one-dimensional models, the weakening of the bulk-boundary correspondence, due to the important correlations between bulk and edges, and consequently to clarify the nature of the massive edge states appearing in the topological LR. The emergence of this peculiar edge structure is signaled by the bulk ES. The stability of the LRP against finite-size effects, relevant in current experiments, and against local disorder is discussed, showing that the latter ingredient can even strengthen the effect of the LR couplings. Finally, we analyze the entanglement content of the paradigmatic LR Ising spin chain, inferring again important deviations from the SR regime, and the limitations of bulk-boundary (tensor-network based) approaches to classify LR spin models

Edge insulating topological phases in a two-dimensional long-range superconductor

We study the zero-temperature phase diagram of a two dimensional square lattice loaded by spinless fermions, with nearest neighbor hopping and algebraically decaying pairing. We find that for sufficiently long-range pairing, new phases, not continuously connected with any short-range phase, occur, signaled by the violation of the area law for the Von Neumann entropy, by semi-integer Chern numbers, and by edge modes with nonzero mass. The latter feature results in the absence of single-fermion edge conductivity, present instead in the short- range limit. The definition of a topology in the bulk and the presence of a bulk-boundary correspondence is still suggested for the long-range phases. Recent experimental proposals and advances open the stimulating possibility to probe the described long-range effects in next-future realistic set-ups

Discriminating Interactions Between Chiral Molecules In the Liquid-phase - Effect On Volumetric Properties

Volume changes on mixing for binary mixtures of optically active liquid compounds have been determined at 25 "C by using a vibrating tube densimeter. Six enantiomeric and six nonenantiomeric pairs of chiral molecules have been considered. In all the cases chiral discrimination appeared to produce small but significant effects (0.0024.016 cm3 mol-'). The excess molar volumes, p, of the (+) and (-) isomers of limonene, carvone, 2-methyl-1-butanol, and a-methylbenzylamine showed negative values, while VE of the enantiomers of a-pinene and 2-odanol gave positive results. Partial molar volumes, Po,fo r the investigated chiral solutes in chiral solvents have been obtained from p data. The effecta of chiral discrimination of Po have been compared with the prediction of a simple statistical approach in which discrimination arises from space-filling differences in contacts between hard surfaces

Two-kink bound states in the magnetically perturbed Potts field theory at T<Tc

The q-state Potts field theory with $2\le q\le 4$ in the low-temperature phase is considered in presence of a weak magnetic field h. In absence of the magnetic field, the theory is integrable, but not free at q>2: its elementary excitations - the kinks - interact at small distances, and their interaction can be characterized by the factorizable scattering matrix which was found by Chim and Zamolodchikov. The magnetic field induces the long-range attraction between kinks causing their confinement into the bound-states. We calculate the masses of the two-kink bound states in the leading order in |h| -> 0 expressing them in terms of the scattering matrix of kinks at h=0.Comment: 20 pages, no figures, v2: one section and references adde

Bound state dynamics in the long-range spin- ½ XXZ model

Experimental platforms based on trapped ions, cold molecules, and Rydberg atoms have made possible the investigation of highly nonlocal spin-1/2 Hamiltonians with long-range couplings. Here, we study the effects of such nonlocal couplings in the long-range spin-1/2 XXZ Heisenberg Hamiltonian. We calculate explicitly the two-spin energy spectrum, which describes all possible energetic configurations of two spins pointing in a specific direction embedded in a background of spins with opposite orientation. For fast decay of the spin-spin couplings, we find that the two-spin energy spectrum is characterized by well-defined discrete values, corresponding to bound states, separated by a set of continuum states describing the scattering region. In the deep long-range regime instead, the bound states disappear as they get incorporated by the scattering region. The presence of two-spin bound states results to be crucial to determine both two- and many-spin dynamics. On one hand, radically different two-spin spreadings can be observed by tuning the decay of the spin couplings. On the other hand, two-spin bound states enable the dynamical stabilization of effective antiferromagnetic states in the presence of ferromagnetic couplings. Finally, we propose a novel scheme based on a trapped-ion quantum simulator to experimentally realize the long-range XXZ model and to study its out-of-equilibrium properties

Collision of impurities with Bose-Einstein condensates

open5noQuantum dynamics of impurities in a bath of bosons is a long-standing problem of solid-state, plasma, and atomic physics. Recent experimental and theoretical investigations with ultracold atoms focused on this problem, studying atomic impurities immersed in a atomic Bose-Einstein condensate (BEC) and for various relative coupling strengths tuned by the Fano-Feshbach resonance technique. Here we report extensive numerical simulations on a closely related problem: the collision between a bosonic impurity made of few 41K atoms and a BEC made of 87Rb atoms in a quasi one-dimensional configuration and under a weak harmonic axial confinement. For small values of the interspecies interaction strength (no matter the sign of it), we find that the impurity, which starts from outside the BEC, simply oscillates back and forth the BEC cloud, but the frequency of oscillation depends on the interaction strength. For intermediate couplings, after a few cycles of oscillation the impurity is captured by the BEC and strongly changes its amplitude of oscillation. In the strong interaction regime, if the interspecies interaction is attractive, a local maximum (bright soliton) in the density of BEC occurs where the impurity is trapped; instead, if the interspecies interaction is repulsive, the impurity is not able to enter in the BEC cloud and the reflection coefficient is close to one. On the other hand, if the initial displacement of the impurity is increased, the impurity is able to penetrate in the cloud leading to the appearance of a moving hole (dark soliton) in the BEC.openLingua, F.; Lepori, L.; Minardi, F.; Penna, V.; Salasnich, L.Lingua, F.; Lepori, Luca; Minardi, F.; Penna, V.; Salasnich, L