Recent results on integrable electronic models

We review the approach of generalized permutator to produce a class of integrable quantum Hamiltonians, as well as the technique of Sutherland species (SS) to map a subclass of it into solvable spinless fermions models. In particular, we apply the above scheme to construct integrable interacting electron Hamiltonians: first we review the extended Hubbard case, discussing both ground state and thermodynamics; then we pass to constrained fermion models, generating 56 integrable cases, among which both supersymmetric t-J model and infinite U Hubbard model are obtained, as well as other physically interesting cases, such as a particular t-V model. For the latter we describe how the complete spectrum can be gained by means of SS technique. Finally we speculate about possible applications to spin S models.Comment: Review article; 12 pages, 4 figures. Appeared on Recent Research Developements in Physics 5, 513-534 (Transworld Research Network, India, 2004

Entanglement in extended Hubbard models and quantum phase transitions

The role of two-point and multipartite entanglement at quantum phase transitions (QPTs) in correlated electron systems is investigated. We consider a bond-charge extended Hubbard model exactly solvable in one dimension which displays various QPTs, with two (qubit) as well as more (qudit) on-site degrees of freedom involved. The analysis is carried out by means of appropriate measures of bipartite/multipartite quantum correlations. It is found that all transitions ascribed to two-point correlations are characterized by an entanglement range which diverges at the transition points. The exponent coincides with that of the correlation length at the transitions. We introduce the correlation ratio, namely, the ratio of quantum mutual information and single-site entanglement. We show that at T=0, it captures the relative role of two-point and multipartite quantum correlations at transition points, generalizing to qudit systems the entanglement ratio. Moreover, a finite value of quantum mutual information between infinitely distant sites is seen to quantify the presence of off-diagonal long-range order induced by multipartite entanglement.Comment: 14 pages, 8 figures, 2 table

Detecting the tunneling rates for strongly interacting fermions on optical lattices

Strongly interacting fermionic atoms on optical lattices are studied through a Hubbard-like model Hamiltonian, in which tunneling rates of atoms and molecules between neighboring sites are assumed to be different. In the limit of large onsite repulsion U, the model is shown to reproduce the t-J Hamiltonian, in which the J coefficient of the Heisenberg term depends on the particle-assisted tunneling rate g: explicitly, $J=4 g^2/U$. At half-filling, g drives a crossover from a Brinkman-Rice paramagnetic insulator of fully localized atoms (g=0) to the antiferromagnetic Mott insulator of the standard Hubbard case (g=t). This is observed already at the intermediate coupling regime in the number of doubly occupied sites, thus providing a criterion to extract from measurements the effective value of g.Comment: 5 pages, 3 figure

Spin-fermion mappings for even Hamiltonian operators

We revisit the Jordan-Wigner transformation, showing that --rather than a non-local isomorphism between different fermionic and spin Hamiltonian operators-- it can be viewed in terms of local identities relating different realizations of projection operators. The construction works for arbitrary dimension of the ambient lattice, as well as of the on-site vector space, generalizing Jordan-Wigner's result. It provides direct mapping of local quantum spin problems into local fermionic problems (and viceversa), under the (rather physical) requirement that the latter are described by Hamiltonian's which are even products of fermionic operators. As an application, we specialize to mappings between constrained-fermions models and spin 1 models on chains, obtaining in particular some new integrable spin Hamiltonian, and the corresponding ground state energies.Comment: 7 pages, ReVTeX file, no figure

Nanoscale phase separation and superconductivity in the one-dimensional Hirsch model

We investigate numerically at various fillings the ground state of the one-dimensional Hubbard model with correlated hopping x (Hirsch model). It is found that, for a wide range of filling values n around half filling, and for repulsive Coulomb interaction u\leq u_c(x,n), phase separation at a nanoscale (NPS phase) between two conducting phases at different densities occurs when x\gtrsim 2/3. The NPS phase is accompanied by the opening of a spin gap and the system behaves as a Luther-Emery Liquid with dominant superconducting correlations. Close to half filling, an anomalous peak emerges in the charge structure factor related to the density of doubly occupied sites, which determines the size of the droplets in the NPS phase. For 1/2\lesssim x\lesssim 2/3 a crossover to a homogeneous phase, still superconducting, takes place.Comment: 9 pages, 10 figure

Intercomparison of 3D turbulence parameterizations for dispersion models in complex terrain derived from a circulation model

A procedure for estimating 3D turbulent parameters from the outputs of a circulation model to be used as input of a random flight model for complex terrain dispersion simulation is presented. It is based on parameterization schemes for surface layer parameters and wind velocity standard deviation profiles available in the literature. The predictions of various schemes (two for surface layer quantities and three either for the PBL depth or standard deviation profiles) have been compared to observations carried out in the alpine region (south Switzerland) during the second TRANSALP campaign by three Doppler Sodar and two sonic anemometers

FFLO oscillations and magnetic domains in the Hubbard model with off-diagonal Coulomb repulsion

We observe the effect of non-zero magnetization m onto the superconducting ground state of the one dimensional repulsive Hubbard model with correlated hopping X. For t/2 < X < 2t/3, the system first manifests Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) oscillations in the pair-pair correlations. For m = m1 a kinetic energy driven macroscopic phase separation into low-density superconducting domains and high-density polarized walls takes place. For m > m2 the domains fully localize, and the system eventually becomes a ferrimagnetic insulator.Comment: IOP RevTeX class, 18 pages, 13 composite *.eps figure

Two-Point Versus Multipartite Entanglement in Quantum Phase Transitions

We analyze correlations between subsystems for an extended Hubbard model exactly solvable in one dimension, which exhibits a rich structure of quantum phase transitions (QPTs). The T=0 phase diagram is exactly reproduced by studying singularities of single-site entanglement. It is shown how comparison of the latter quantity and quantum mutual information allows one to recognize whether two-point or shared quantum correlations are responsible for each of the occurring QPTs. The method works in principle for any number D of degrees of freedom per site. As a by-product, we are providing a benchmark for direct measures of bipartite entanglement; in particular, here we discuss the role of negativity at the transition.Comment: 4 pages, 2 figures, 1 tabl

Momentum-space analysis of multipartite entanglement at quantum phase transitions

We investigate entanglement properties at quantum phase transitions of an integrable extended Hubbard model in the momentum space representation. Two elementary subsystems are recognized: the single mode of an electron, and the pair of modes (electrons coupled through the eta-pairing mechanism). We first detect the two/multi-partite nature of each quantum phase transition by a comparative study of the singularities of Von Neumann entropy and quantum mutual information. We establish the existing relations between the correlations in the momentum representation and those exhibited in the complementary picture: the direct lattice representation. The presence of multipartite entanglement is then investigated in detail through the Q-measure, namely a generalization of the Meyer-Wallach measure of entanglement. Such a measure becomes increasingly sensitive to correlations of a multipartite nature increasing the size of the reduced density matrix. In momentum space, we succeed in obtaining the latter for our system at arbitrary size and we relate its behaviour to the nature of the various QPTs.Comment: 8 pages, 4 figure

Cooper pairs and exclusion statistics from coupled free-fermion chains

We show how to couple two free-fermion chains so that the excitations consist of Cooper pairs with zero energy, and free particles obeying (mutual) exclusion statistics. This behavior is reminiscent of anyonic superconductivity, and of a ferromagnetic version of the Haldane-Shastry spin chain, although here the interactions are local. We solve this model using the nested Bethe ansatz, and find all the eigenstates; the Cooper pairs correspond to exact-string or ``0/0'' solutions of the Bethe equations. We show how the model possesses an infinite-dimensional symmetry algebra, which is a supersymmetric version of the Yangian symmetry algebra for the Haldane-Shastry model.Comment: 16 pages. v2: includes explicit expression for super-Yangian generato