Finite-size corrections to entanglement in quantum critical systems

We analyze the finite-size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite-size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system L -> infinity) exhibit a unique pattern of entanglement, which differ only at leading order (1/L)(2). In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length L for both periodic and twisted boundary conditions.

Two-dimensional photonic crystals in antimony-based films fabricated by holography

In this work, we demonstrated the fabrication of two-dimensional (2D) photonic crystals layers (2D-PCLs) by combining holographic recording and the evaporation of antimony-based glasses. Such materials present high refractive indices that can be tuned from 1.8 to 2.4, depending on the film composition; thus, they are interesting dielectric materials for fabrication of 2D-PCLs. The good quality of the obtained samples allowed the measurement of their PC properties through the well-defined Fano resonances that appear in the transmittance spectrum measurements at different incidence angles. The experimental results are in good agreement with the calculated band diagram for the hexagonal asymmetric structure. (C) 2008 American Institute of Physics.

Energy spectra for quantum wires and two-dimensional electron gases in magnetic fields with Rashba and Dresselhaus spin-orbit interactions

We introduce an analytical approximation scheme to diagonalize parabolically confined two-dimensional (2D) electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and noncrossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength k(R)l of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e. g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the nth Landau-level g(n) factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.

Effect of spatial inhomogeneity on the mapping between strongly interacting fermions and weakly interacting spins

A combined analytical and numerical study is performed of the mapping between strongly interacting fermions and weakly interacting spins, in the framework of the Hubbard, t-J, and Heisenberg models. While for spatially homogeneous models in the thermodynamic limit the mapping is thoroughly understood, we here focus on aspects that become relevant in spatially inhomogeneous situations, such as the effect of boundaries, impurities, superlattices, and interfaces. We consider parameter regimes that are relevant for traditional applications of these models, such as electrons in cuprates and manganites, and for more recent applications to atoms in optical lattices. The rate of the mapping as a function of the interaction strength is determined from the Bethe-Ansatz for infinite systems and from numerical diagonalization for finite systems. We show analytically that if translational symmetry is broken through the presence of impurities, the mapping persists and is, in a certain sense, as local as possible, provided the spin-spin interaction between two sites of the Heisenberg model is calculated from the harmonic mean of the onsite Coulomb interaction on adjacent sites of the Hubbard model. Numerical calculations corroborate these findings also in interfaces and superlattices, where analytical calculations are more complicated.

Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit (L=0) by explicitly including the effect of the second, L=1, Landau level and arbitrary spin polarization. The inclusion of the L=1 level brings the fields to which the formula applies closer to the laboratory range, as compared to previous expressions, valid only for L=0 and complete spin polarization. We identify and explain two distinct regimes separated by a critical density n(c). Below n(c), the per particle exchange energy is lowered by the contribution of L=1, whereas above n(c) it is increased. As special cases of our general equation we recover various known more limited results for higher fields, and we identify and correct a few inconsistencies in some of these earlier expressions.

Constraints on the infrared behavior of the gluon propagator in Yang-Mills theories

We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case, we find D(0)=0, in agreement with Maas. We suggest an explanation for these results. We note that our discussion is general, although we apply our analysis only to pure gauge theory in the Landau gauge. Simulations have been performed on the IBM supercomputer at the University of Sao Paulo.

ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

POLAR ACTIONS ON CERTAIN PRINCIPAL BUNDLES OVER SYMMETRIC SPACES OF COMPACT TYPE

We study polar actions with horizontal sections on the total space of certain principal bundles G/K -> G/H with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we exhibit examples of hyperpolar actions with cohomogeneity greater than one on locally irreducible homogeneous spaces with nonnegative curvature which are not homeomorphic to symmetric spaces.

Full-dimensional analytical ab initio potential energy surface of the ground state of HOI

Extensive ab initio calculations using a complete active space second-order perturbation theory wavefunction, including scalar and spin-orbit relativistic effects with a quadruple-zeta quality basis set were used to construct an analytical potential energy surface (PES) of the ground state of the [H, O, I] system. A total of 5344 points were fit to a three-dimensional function of the internuclear distances, with a global root-mean-square error of 1.26 kcal mol(-1). The resulting PES describes accurately the main features of this system: the HOI and HIO isomers, the transition state between them, and all dissociation asymptotes. After a small adjustment, using a scaling factor on the internal coordinates of HOI, the frequencies calculated in this work agree with the experimental data available within 10 cm(-1). (C) 2011 American Institute of Physics. [doi: 10.1063/1.3615545]

Sodium piperidine-1-carbodithioate dihydrate

The asymmetric unit of the title compound, Na(+)center dot C(6)H(10)NS(2) center dot 2H(2)O, is composed of a sodium cation, a piperidinedithiocarbamate anion which exhibits positional disorder, and two lattice water molecules. The atoms of the piperidine ring are divided over two sites with occupancy factors of 0.554 (6) and 0.446 (6). In the crystal, the sodium cation (coordination number of 6) and the piperidinedithiocarbamate anion are linked, forming an infinite two-dimensional network extending parallel to (001). O-H center dot center dot center dot S hydrogen bonds, involving the lattice water molecules, also aid in stabilizing the crystal sructure.

Ammonium piperidine-1-carbodithioate

The title compound, NH(4) +center dot C(6)H(10)NS(2) -, is composed of an ammonium cation and a piperidine-1-carbodithioate anion which exhibits positional disorder. The atoms of the ring have a structural disorder and they are divided into two sites, with occupancy factors of 0.584 and 0.426.. In the crystal, the cation and anion are linked by N-H...S hydrogen bonds to form an infinite two-dimensional network.

Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)