Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

Half-Filled Layered Organic Superconductors and the Resonating-Valence-Bond Theory of the Hubbard-Heisenberg Model

We present a resonating-valence-bond theory of superconductivity for the Hubbard-Heisenberg model on an anisotropic triangular lattice. Our calculations are consistent with the observed phase diagram of the half-filled layered organic superconductors, such as the beta, beta('), kappa, and lambda phases of (BEDT-TTF)(2)X [bis(ethylenedithio)tetrathiafulvalene] and (BETS)(2)X [bis(ethylenedithio)tetraselenafulvalene]. We find a first order transition from a Mott insulator to a d(x)(2)-y(2) superconductor with a small superfluid stiffness and a pseudogap with d(x)(2)-y(2) symmetry.

Exact solution of the A(n-1)((1)) trigonometric vertex model with non-diagonal open boundaries

The A(n-1)((1)) trigonometric vertex model with generic non-diagonal boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property. (C) 1998 Elsevier Science B.V.

Sharp vibronic spectra of Cu(II) doped Cs2ZrCl6

The low temperature electronic spectrum of Cu(II) doped Cs2ZrCl6 is reported. It is found that Cu(II) is incorporated as the square planar copper tetrachloride ion, CuCl42-, which substitutes at the Zr(IV) site in the Cs2ZrCl6 lattice. There is a complete absence of axial coordination. The optical spectrum shows vibronic structure with peak widths as small as 8 cm(-1), far narrower than previously seen for this ion. The energy of the observed transitions and the Franck-Condon intensity pattern suggest that there is a substantial relaxation of the host lattice about the impurity ion. The relative intensity of the magnetic dipole component of the bands appears to be considerably greater than for pure copper(II) compounds containing the CuCl42- ion. (C) 1998 Elsevier Science B.V. All rights reserved.

Aminotriazines as locking fragments in macrocyclic synthesis

The macrocyclic compounds (6-(4',6'-diamino-1',3',5'-triazinyl)-1,4,6,8,11-pentaazacyclotetradecane)copper(II) triperchlorate dihydrate, [Cu(HL2)](ClO4)(3). 2H(2)O, (6-(6'-amino-4'-oxo-1'H-1',3',5'-triazinyl)-1,4,6,8,11-pentaazacyclotetradecane)copper(II) diperchlorate hydrate, [CuL3](ClO4)(2). H2O, and [(6-(4',6'-dioxo-1'H-1',3',5'-triazinyl) 1,4,6,8,11-pentaazacyclotetradecane)copper(II)] diperchlorate, [CuL4](ClO4)(2), have been synthesized. The macrocycles synthesized contain respectively pendant melamine, ammeline,and ammelide rings. The X-ray cyrstallographic analyses of [Cu(HL2)](ClO4)(3). 2H(2)O, triclinic, space group P (1) over bar, a = 9.489(10) Angstrom, b = 12.340(2) Angstrom, c = 24.496(4) Angstrom, alpha = 87.74(10)degrees beta = 85.51(10)degrees gamma = 70.95(10)degrees and Z = 4, and {[CuL3](ClO4)(2). H2O}2, monoclinic, space group C2/c, a = 18.624(8) Angstrom, b = 17.160(2) Angstrom, c = 15.998(6) Angstrom, beta = 117.82(2)degrees, and Z = 4, are reported. The structure of [Cu(HL2)](ClO4)(3). 2H(2)O shows the formation of linear tapes, formed by a combination of hydrogen bonds and pi-pi stacking interactions. The structure of [CuL3](ClO4)(2). H2O displays formation of dimers, formed by a coordinate bond from the oxygen in one molecule to the copper atom of another. The tautomeric forms of the ammeline and ammelide moieties have been determined. The potential of these compounds as subunits for cocrystallization has been investigated.

An evaluation of the time dependence of the anisotropy of the water diffusion tensor in acute human ischemia

We have performed MRI examinations to determine the water diffusion tensor in the brain of six patients who were admitted to the hospital within 12 h after the onset of cerebral ischemic symptoms. The examinations have been carried out immediately after admission, and thereafter at varying intervals up to 90 days post admission. Maps of the trace of the diffusion tensor, the fractional anisotropy and the lattice index, as well as maps of cerebral blood perfusion parameters, were generated to quantitatively assess the character of the water diffusion tensor in the infarcted area. In patients with significant perfusion deficits and substantial lesion volume changes, four of six cases, our measurements show a monotonic and significant decrease in the diffusion anisotropy within the ischemic lesion as a function of time. We propose that retrospective analysis of this quantity, in combination with brain tissue segmentation and cerebral perfusion maps, may be used in future studies to assess the severity of the ischemic event. (C) 1999 Elsevier Science Inc.

Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field

We present some exact results for the effect of disorder on the critical properties of an anisotropic XY spin chain in a transverse held. The continuum limit of the corresponding fermion model is taken and in various cases results in a Dirac equation with a random mass. Exact analytic techniques can then be used to evaluate the density of states and the localization length. In the presence of disorder the ferromagnetic-paramagnetic or Ising transition of the model is in the same universality class as the random transverse field Ising model solved by Fisher using a real-space renormalization-group decimation technique (RSRGDT). If there is only randomness in the anisotropy of the magnetic exchange then the anisotropy transition (from a ferromagnet in the x direction to a ferromagnet in the y direction) is also in this universality class. However, if there is randomness in the isotropic part of the exchange or in the transverse held then in a nonzero transverse field the anisotropy transition is destroyed by the disorder. We show that in the Griffiths' phase near the Ising transition that the ground-state energy has an essential singularity. The results obtained for the dynamical critical exponent, typical correlation length, and for the temperature dependence of the specific heat near the Ising transition agree with the results of the RSRODT and numerical work. [S0163-1829(99)07125-8].

New integrable model of correlated electrons with off-diagonal long-range order from so(5) symmetry

We present a new integrable model for correlated electrons which is based on so(5) symmetry. By using an eta-pairing realization we construct eigenstates of the Hamiltonian with off-diagonal long-range order. It is also shown that these states lie in the ground state sector. We exactly solve the model on a one-dimensional lattice by the Bethe ansatz.

Single-spin measurement using single-electron transistors to probe two-electron systems

We present a method for measuring single spins embedded in a solid by probing two-electron systems with a single-electron transistor (SET). Restrictions imposed by the Pauli principle on allowed two-electron states mean that the spin state of such systems has a profound impact on the orbital states (positions) of the electrons, a parameter which SET's are extremely well suited to measure. We focus on a particular system capable of being fabricated with current technology: a Te double donor in Si adjacent to a Si/SiO2, interface and lying directly beneath the SET island electrode, and we outline a measurement strategy capable of resolving single-electron and nuclear spins in this system. We discuss the limitations of the measurement imposed by spin scattering arising from fluctuations emanating from the SET and from lattice phonons. We conclude that measurement of single spins, a necessary requirement for several proposed quantum computer architectures, is feasible in Si using this strategy.

Transport properties of strongly correlated metals: A dynamical mean-field approach

The temperature dependence of the transport properties of the metallic phase of a frustrated Hubbard model on the hypercubic lattice at half-filling is calculated. Dynamical mean-held theory, which maps the Hubbard model onto a single impurity,Anderson model that is solved self-consistently, and becomes exact in the limit of large dimensionality, is used. As the temperature increases there is a smooth crossover from coherent Fermi liquid excitations at low temperatures to incoherent excitations at high temperatures. This crossover leads to a nonmonotonic temperature dependence for the resistance, thermopower, and Hall coefficient, unlike in conventional metals. The resistance smoothly increases from a quadratic temperature dependence at low temperatures to large values which can exceed the Mott-Ioffe-Regel value ha/e(2) (where a is a lattice constant) associated with mean free paths less than a lattice constant. Further signatures of the thermal destruction of quasiparticle excitations are a peak in the thermopower and the absence of a Drude peak in the optical conductivity. The results presented here are relevant to a wide range of strongly correlated metals, including transition metal oxides, strontium ruthenates, and organic metals.

Adhesion of microbes using 3-aminopropyl triethoxy silane and specimen stabilisation techniques for analytical transmission electron microscopy

A variety of adhesive support-films were tested for their ability to adhere various biological specimens for transmission electron microscopy. Support films primed with 3-amino-propyl triethoxy silane (APTES), poly-L-lysine, carbon and ultraviolet-B (UV-B)-irradiated carbon were tested for their ability to adhere a variety of biological specimens including axenic cultures of Bacillus subtilis and Escherichia coli and wild-type magnetotactic bacteria. The effects of UV-B irradiation on the support film in the presence of air and electrostatic charge on primer deposition were tested and the stability of adhered specimens on various surfaces was also compared. APTES-primed UV-B-irradiated Pioloform(TM) was consistently the best adhesive, especially for large cells, and when adhered specimens were UV-B irradiated they became remarkably stable under an electron beam. This assisted the acquisition of in situ phase-contrast lattice images from a variety of biominerals in magnetotactic bacteria, in particular metastable greigite magnetosomes. Washing tests indicated that specimens adhering to APTES-primed UV-B-irradiated Pioloform(TM) were covalently coupled. The electron beam stability was hypothesised to be the result of mechanical strengthening of the specimen and support film and the reduced electrical resistance in the specimen and support film due to their polymerization and covalent coupling.

Cyclotron effective masses in layered metals

Many layered metals such as quasi-two-dimensional organic molecular crystals show properties consistent with a Fermi-liquid description at low temperatures. The effective masses extracted from the temperature dependence of the magnetic oscillations observed in these materials are in the range, m(c)*/m(e) similar to 1 - 7, suggesting that these systems are strongly correlated. However, the ratio m(c)*/m(e) contains both the renormalization due to the electron-electron interaction and the periodic potential of the lattice. We show that for any quasi-two-dimensional band structure, the cyclotron mass is proportional to the density-of-states at the Fermi energy. Due to Luttinger's theorem, this result is also valid in the presence of interactions. We then evaluate m(c) for several model band structures for the beta, kappa, and theta families of (BEDT-TTF)(2)X, where BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene) and X is an anion. We find that for kappa-(BEDT-TTF)(2)X, the cyclotron mass of the beta orbit, m(c)*(beta) is close to 2 m(c)*(alpha), where m(c)*(alpha) is the effective mass of the alpha orbit. This result is fairly insensitive to the band-structure details. For a wide range of materials we compare values of the cyclotron mass deduced from band-structure calculations to values deduced from measurements of magnetic oscillations and the specific-heat coefficient gamma.

Labelled tableaux for non-normal modal logics

In this paper we show how to extend KEM, a tableau-like proof system for normal modal logic, in order to deal with classes of non-normal modal logics, such as monotonic and regular, in a uniform and modular way.

Charge ordering and antiferromagnetic exchange in layered molecular crystals of the theta type

We consider the electronic properties of layered molecular crystals of the type theta -D(2)A where A is an anion and D is a donor molecule such as bis-(ethylenedithia-tetrathiafulvalene) (BEDT-TTF), which is arranged in the theta -type pattern within the layers. We argue that the simplest strongly correlated electron model that can describe the rich phase diagram of these materials is the extended Hubbard model on the square lattice at one-quarter filling. In the limit where the Coulomb repulsion on a single site is large, the nearest-neighbor Coulomb repulsion V plays a crucial role. When V is much larger than the intermolecular hopping integral t the ground state is an insulator with charge ordering. In this phase antiferromagnetism arises due to a novel fourth-order superexchange process around a plaquette on the square lattice. We argue that the charge ordered phase is destroyed below a critical nonzero value V, of the order of t. Slave-boson theory is used to explicitly demonstrate this for the SU(N) generalization of the model, in the large-N limit. We also discuss the relevance of the model to the all-organic family beta-(BEDT-TTF)(2)SF5YSO3 where Y=CH2CF2, CH2, CHF.