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

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

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

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

Structure of quantum correlations in momentum space and off diagonal long range order in eta pairing and BCS states

The quantum states built with the eta paring mechanism i.e., eta pairing states, were first introduced in the context of high temperature superconductivity where they were recognized as important example of states allowing for off-diagonal long-range order (ODLRO). In this paper we describe the structure of the correlations present in these states when considered in their momentum representation and we explore the relations between the quantum bipartite/multipartite correlations exhibited in k space and the direct lattice superconducting correlations. In particular, we show how the negativity between paired momentum modes is directly related to the ODLRO. Moreover, we investigate the dependence of the block entanglement on the choice of the modes forming the block and on the ODLRO; consequently we determine the multipartite content of the entanglement through the evaluation of the generalized "Meyer Wallach" measure in the direct and reciprocal lattice. The determination of the persistency of entanglement shows how the network of correlations depicted exhibits a self-similar structure which is robust with respect to "local" measurements. Finally, we recognize how a relation between the momentum-space quantum correlations and the ODLRO can be established even in the case of BCS states.Comment: 11 pages, 3 figure

Statistical analysis of three series of daily rainfall in North-Western Italy

In this work we study three long series of daily rainfall measured in North-Western Italy. We analyze the global statistical properties of the three data sets and we discuss both the seasonal distribution of rainfall intensity and the long-term variation in rainfall properties. We show that the three series display a vanishingly small autocorrelation for periods longer than one or two days, consistent with the absence of multifractality in these records. These time series are largely consistent with the output of a simple chain-dependent stochastic process

The Potential Role of miRNAs in SARS-CoV-2 Infection Prognosis: An in-Silico Approach

https://openworks.mdanderson.org/sumexp21/1148/thumbnail.jp

Symmetry breaking effects upon bipartite and multipartite entanglement in the XY model

We analyze the bipartite and multipartite entanglement for the ground state of the one-dimensional XY model in a transverse magnetic field in the thermodynamical limit. We explicitly take into account the spontaneous symmetry breaking in order to explore the relation between entanglement and quantum phase transitions. As a result we show that while both bipartite and multipartite entanglement can be enhanced by spontaneous symmetry breaking deep into the ferromagnetic phase, only the latter is affected by it in the vicinity of the critical point. This result adds to the evidence that multipartite, and not bipartite, entanglement is the fundamental indicator of long range correlations in quantum phase transitions.Comment: 13 pages, 19 figures, comments welcome. V2: small changes, published versio

A model based on Heisenberg’s theory for the eddy diffusivity in decaying turbulence applied to the residual layer

The problemof the theoretical derivation of a parameterization for the eddy diffusivity in decaying turbulence is addressed. This derivation makes use of the dynamical equation for the energy spectrum density and the classical statistical diffusion theory. The starting point is Heisenberg’s elementary decaying turbulence theory. The main assumption is related to the identification of a frequency, lying in the inertial subrange, characterizing the inertial energy transfer among eddies of different size. The resulting eddy diffusivity parameterization is then applied to the decay of convective turbulence in the residual layer. Besides the intrinsic scientific interest, this topic has relevance for mesoscale transport and diffusion simulations. The resulting expression for the eddy diffusivity cannot be solved analytically. For this reason an algebraic approximated formulation, giving nearly the same results as the exact expression, is also proposed

Estimation of emission rate from experimental data

The estimation of the source pollutant strength is a relevant issue for atmospheric environment. This characterizes an inverse problem in the atmospheric pollution dispersion studies. In the inverse analysis, a time-dependent pollutant source is considered, where the location of such source term is assumed known. The inverse problem is formulated as a non-linear optimization approach, whose objective function is given by the least-square difference between the measured and simulated by the mathematical model, pollutant concentration, associated with a regularization operator. The forward problem is addressed by a Lagrangian model, and a quasi-Newton method is employed for minimizing the objective function. The second-order Tikhonov regularization is applied and the regularization parameter is computed by using the L-curve scheme. The inverse-problem methodology is verified with data from the tracer Copenhagen experiment