51 research outputs found
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
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, . 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
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
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
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
Mobility of Scientists across Europe: The Role Played by European Research Funding
The European Research Council has provided substantial research grants across all disciplines during the period 2007–2013. An analysis of the distribution of the ERC (IDEAS) Starting, Consolidator and Advanced grants shows substantial differences by country. On the one hand, the UK excels in the relative number of awards, in its share among the top receiving institutions, in a high proportion of inwards mobile scholars and in the overall financial gain through ERC as compared with the UK's contribution to the EU budget. In addition, the Netherlands is among the winners in these respects. On the other hand, Italy fares unfavourably according to these measures. In the search for an explanation of the Italian situation, a comparison is undertaken with other European countries of a similar size. The article arrives at the conclusion that low Italian success in efforts to raise such ERC funds is not due to the low average quality of the Italian education and research system, but rather due to low funding, e.g. to a low proportion of the GDP spent on research
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
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
Single-site entanglement at superconductor-insulator transition in the Hirsch model
We investigate the transition to the insulating state in the one-dimensional
Hubbard model with bond-charge interaction x (Hirsch model), at half-filling
and T=0. By means of the density-matrix renormalization group algorithm the
charge gap closure is examined by both standard finite size scaling analysis
and looking at singularities in the derivatives of single-site entanglement.
The results of the two techniques show that a quantum phase transition takes
place at a finite Coulomb interaction u_c(x) for x>0.5. The region 0<u<u_c
turns out to have a superconducting nature, at least for not too large x>x_c.Comment: 5 pages, 6 figure
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
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