Eight-state supersymmetric U model of strongly correlated fermions

An integrable eight-state supersymmetric U model is proposed, which is a fermion model with correlated single-particle and pair hoppings as well as uncorrelated triple-particle hopping. It has a gl(3/1) supersymmetry and contains one symmetry-preserving free parameter. The model is solved and the Bethe ansatz equations are obtained. [S0163-1829(98)00616-X].

Iron(III) and iron(II) complexes of 1-thia-4,7-diazacyclononane ([9]aneN(2)S) and 1,4-dithia-7-azacyclononane ([9]aneNS(2)). X-Ray structural analyses, magnetic susceptibility, Mossbauer, EPR and electronic spectroscopy

The complexes [Fe([9]aneN(2)S)(2)][ClO4](2), [Fe([9]aneN(2)S)(2)][ClO4](3) and [Fe([9]aneNS(2))(2)][ClO4](2) ([9]aneN(2)S = 1-thia-4. 7-diazacyclononane and [9]aneNS(2) = 1,4-dithia-7-azacyclononane) have been prepared and the latter two characterised by X-ray crystallography. The Mossbauer spectra (isomer shift/mm s(-1), quadrupole splitting/mm s(-1), 4.2 K) for [Fe([9]aneN(2)S)(2)][ClO4](2) (0.52, 0.57), [Fe([9]aneN(2)S)(2)][ClO4](3) (0.25, 2.72) and [Fe([9]aneNS(2))(2)][ClO4](2) (0.43, 0.28) are typical for iron(II) and iron(III) complexes. Variable-temperature susceptibility measurements for [Fe([9]aneN(2)S)(2)][ClO4](2) (2-300 K) revealed temperature-dependent behaviour in both the solid state [2.95 mu(B) (300 K)-0.5 mu(B) (4.2 K)] and solution (Delta H degrees 20-22 kJ mol(-1), Delta S degrees 53-60 J mol(-1) K-1). For [Fe([9]aneN(2)S)(2)][ClO4](3) in the solid state [2.3 mu(B) (300 K)-1.9 mu(B) (4.2 K)] the magnetic data were fit to a simple model (H = -lambda L . S + mu L-z) to give the spin-orbit coupling constant (lambda) of -260 +/- 10 cm(-1). The solid-state X-band EPR spectrum of [Fe([9]aneN(2)S)(2)][ClO4](3) revealed axial symmetry (g(perpendicular to) = 2.607, g(parallel to) = 1.599). Resolution of g(perpendicular to) into two components at Q-band frequencies indicated a rhombic distortion. The low-temperature single-crystal absorption spectra of [Fe([9]aneN(2)S)(2)][ClO4](2) and [Fe([9]aneNS(2))(2)][ClO4](2) exhibited additional bands which resembled pseudotetragonal low-symmetry splitting of the parent octahedral (1)A(1g) --> T-1(2g) and (1)A(1g) ---> T-1(1g) transitions. However, the magnitude of these splittings was too large, requiring 10Dq for the thioether donors to be significantly larger than for the amine donors. Instead, these bands were tentatively assigned to weak, low-energy S --> Fe-II charge-transfer transitions. Above 200 K, thermal occupation of the high-spin T-5(2g) ground state resulted in observation of the T-5(2g) --> E-5(g) transition in the crystal spectrum of [Fe([9]aneN(2)S)(2)][ClO4](2). From a temperature-dependence study, the separation of the low-spin (1)A(1g) and high-spin T-5(2g) ground states was approximately 1700 cm(-1). The spectrum of the iron(III) complex [Fe([9]aneN(2)S)(2)][ClO4](3) is consistent with a low-spin d(5) configuration.

Synthesis of [Cu-2(Me-2[9]aneN(2)S)(2)(OH)(2)] (PF6)(2), a hydroxo-bridged copper(II) complex of N,N '-dimethyl-1-thia-4,7-diazacyclononane (Me-2[9]aneN(2)S). X-ray structural analysis, magnetic susceptibility, EPR and visible spectroscopy

The bis(mu-hydroxo) complex [Cu-2(Me-2[9]aneN(2)S)(2)(OH)(2)](PF6)(2) (Me-2[9]aneN(2)S = N,N'-dimethyl-1-thia-4,7-diazacyclononane) results after reaction of [Cu(Me-2[9]aneN(2)S)(MeCN)] (PF6) with dioxygen at -78 degrees C in acetonitrile. The complex has been characterized by X-ray crystallography: orthorhombic, space group Pnma, with a 18.710(3), b 16.758(2), c 9.593(2) Angstrom, and Z = 4. The structure refined to a final R value of 0.051. The complex contains two copper(II) ions bridged by two hydroxo groups with Cu ... Cu 2.866(1) Angstrom. The solid-state magnetic susceptibility study reveals ferromagnetic coupling, the fitting parameters being J = +46+/-5 cm(-1), g = 2.01+/-0.01 and theta = -0.58+/-0.03 K. The frozen-solution e.p.r. spectrum in dimethyl sulfoxide is characteristic of a monomeric copper(II) ion (g(parallel to) 2.300, g(perpendicular to) 2.063; A(parallel to) 156.2 x 10(-4) cm(-1), A(perpendicular to) 9.0 x 10(-4) cm(-1)) with an N2O2 donor set. Thioether coordination to the copper(II) in solution is supported by the presence of an intense absorption assigned to a sigma(S)-->Cu-II LMCT transition at c. 34000 cm(-1). The single-crystal spectrum of [Cu-2(Me-2[9]aneN(2)S)(2)(OH)(2)] (PF6)(2) (273 K) reveals d-->d transitions at 14500 and 18300 cm(-1) and a weak pi(S)-->Cu-II charge-transfer band at approximately 25000 cm(-1).

Mesoionic pyridopyrimidinylium and pyridooxazinylium olates and non-mesoionic pyridopyrimidinones. Structures in the solid state, solution, and matrices

X-Ray crystal structures, C-13 NMR spectra and theoretical calculations (B3LYP/6-31G*) are reported for the mesoionic (zwitterionic) pyridopyrimidinylium- and pyridooxazinyliumolates 2a, 3a and 5a,b as well as the enol ether 11b and the enamine 11c. The 1-NH compounds like 1a, 2a and 3a exist in the mesoionic form in the crystal and in solution, but the OH tautomers such as 1b and 2b dominate in the gas phase as revealed by the Ar matrix IR spectra in conjunction with DFT calculations. All data indicate that the mesoionic compounds can be regarded as intramolecular pyridine-ketene zwitterions (cf. 16 --> 17) with a high degree of positive charge on the pyridinium nitrogen, a long pyridinium N-CO bond (ca. 1.44-1.49 Angstrom), and normal C=O double bonds (ca. 1.22 Angstrom). All mesoionic compounds exhibit a pronounced tilting of the olate C=O groups (the C=O groups formally derived from a ketene) towards the pyridinium nitrogen, giving NCO angles of 110-118 degrees. Calculations reveal a hydrogen bond with 6-CH, analogous to what is found in ketene-pyridine zwitterions and the C3O2-pyridine complex. The 2-OH tautomers of type 1b, 2b, and 11 also show a high degree of zwitterionic character as indicated by the canonical structures 11 12.

Simultaneous X-ray imaging of plant root growth and water uptake in thin-slab systems

Direct and simultaneous observation of root growth and plant water uptake is difficult because soils are opaque. X-ray imaging techniques such as projection radiography or Computer Tomography (CT) offer a partial alternative to such limitations. Nevertheless, there is a trade-off between resolution, large field-of-view and 3-dimensionality: With the current state of the technology, it is possible to have any two. In this study, we used X-ray transmission through thin-slab systems to monitor transient saturation fields that develop around roots as plants grow. Although restricted to 2-dimensions, this approach offers a large field-of-view together with high spatial and dynamic resolutions. To illustrate the potential of this technology, we grew peas in 1 cm thick containers filled with soil and imaged them at regular intervals. The dynamics of both the root growth and the water content field that developed around the roots could be conveniently monitored. Compared to other techniques such as X-ray CT, our system is relatively inexpensive and easy to implement. It can potentially be applied to study many agronomic problems, such as issues related to the impact of soil constraints (physical, chemical or biological) on root development.

Diverse solid-state and solution structures within a series of hexaamine dicopper(II) complexes

Mono- and dicopper(II) complexes of a series of potentially bridging hexaamine ligands have been prepared and characterized in the solid state by X-ray crystallography. The crystal structures of the following Cu-II complexes are reported: [Cu(HL3)](ClO4)(3), C11H31Cl3CuN6O12, monoclinic, P2(1)/n, a = 8.294(2) Angstrom, b = 18.364(3) Angstrom, c = 15.674(3) Angstrom, beta = 94.73(2)degrees, Z = 4; {[Cu-2(L-4)(CO3)](2)}(ClO4)(4). 4H(2)O, C40H100Cl4Cu4N12O26, triclinic, P (1) over bar, a = 9.4888(8) Angstrom, b=13.353(1) Angstrom,. c = 15.329(1) Angstrom, alpha = 111.250(7)degrees, beta = 90.068(8)degrees, gamma = 105.081(8)degrees, Z=1; [Cu-2(L-5)(OH2)(2)](ClO4)(4), C(13)H(36)Cl(4)Cu(2)Z(6)O(18), monoclinic, P2(1)/c, a = 7.225(2) Angstrom. b = 8.5555(5) Angstrom, c = 23.134(8) Angstrom, beta = 92.37(1)degrees, Z = 2; [Cu-2(L-6)(OH2)(2)](ClO4)(4). 3H(2)O, C14H44Cl4Cu2N6O21, monoclinic, P2(1)/a, a = 15.204(5) Angstrom, b = 7.6810(7) Angstrom, c = 29.370(1) Angstrom, beta = 100.42(2)degrees, Z = 4. Solution spectroscopic properties of the bimetallic complexes indicate that significant conformational changes occur upon dissolution, and this has been probed with EPR spectroscopy and molecular mechanics calculations.

Large-N solutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs2CuCl4 and to the layered organic superconductors kappa-(BEDT-TTF)(2)X (BEDT-TTF bis(ethylene-dithio)tetrathiafulvalene); X anion)

We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the anisotropic triangular lattice in the large-N limit. These two models may describe respectively the magnetic and electronic properties of the family of layered organic materials K-(BEDT-TTF)(2)X, The Heisenberg model is also relevant to the frustrated antiferromagnet, Cs2CuCl4. We find rich phase diagrams for each model. The Sp(N) :antiferromagnet is shown to have five different phases as a function of the size of the spin and the degree of anisotropy of the triangular lattice. The effects of fluctuations at finite N are also discussed. For parameters relevant to Cs2CuCl4 the ground state either exhibits incommensurate spin order, or is in a quantum disordered phase with deconfined spin-1/2 excitations and topological order. The SU(N) Hubbard-Heisenberg model exhibits an insulating dimer phase, an insulating box phase, a semi-metallic staggered flux phase (SFP), and a metallic uniform phase. The uniform and SFP phases exhibit a pseudogap, A metal-insulator transition occurs at intermediate values of the interaction strength.

Universal state inversion and concurrence in arbitrary dimensions

Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. Wootters's concurrence is defined with the help of the superoperator that flips the spin of a qubit. We generalize the spin-flip superoperator to a universal inverter, which acts on quantum systems of arbitrary dimension, and we introduce the corresponding generalized concurrence for joint pure states of D-1 X D-2 bipartite quantum systems. We call this generalized concurrence the I concurrence to emphasize its relation to the universal inverter. The universal inverter, which is a positive, but not completely positive superoperator, is closely related to the completely positive universal-NOT superoperator, the quantum analogue of a classical NOT gate. We present a physical realization of the universal-NOT Superoperator.

Simulation of the influence of rate- and state-dependent friction on the macroscopic behavior of complex fault zones with the lattice solid model

In order to understand the earthquake nucleation process, we need to understand the effective frictional behavior of faults with complex geometry and fault gouge zones. One important aspect of this is the interaction between the friction law governing the behavior of the fault on the microscopic level and the resulting macroscopic behavior of the fault zone. Numerical simulations offer a possibility to investigate the behavior of faults on many different scales and thus provide a means to gain insight into fault zone dynamics on scales which are not accessible to laboratory experiments. Numerical experiments have been performed to investigate the influence of the geometric configuration of faults with a rate- and state-dependent friction at the particle contacts on the effective frictional behavior of these faults. The numerical experiments are designed to be similar to laboratory experiments by DIETERICH and KILGORE (1994) in which a slide-hold-slide cycle was performed between two blocks of material and the resulting peak friction was plotted vs. holding time. Simulations with a flat fault without a fault gouge have been performed to verify the implementation. These have shown close agreement with comparable laboratory experiments. The simulations performed with a fault containing fault gouge have demonstrated a strong dependence of the critical slip distance D-c on the roughness of the fault surfaces and are in qualitative agreement with laboratory experiments.

Electron exchange coupling for single-donor solid-state spin qubits

Intervalley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighboring phosphorus donor electron states in silicon [B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 88, 027903 (2002); Phys. Rev. B 66, 115201 (2002)]. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction of silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wave functions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller, Hu, and Das Sarma, significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighboring donors that have been implanted into the silicon substrate using an 15 keV ion beam in the so-called top down fabrication scheme for a Kane solid-state quantum computer. In addition, we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wave functions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighboring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller, Hu, and Das Sarma.

Low-temperature single-crystal Raman and neutron-diffraction study of the hydrogenous ammonium copper(II) tutton salt and the deuterated analogue in the metastable state

Low-temperature (15 K) single-crystal neutron-diffraction structures and Raman spectra of the salts (NX4)(2)[CU(OX2)(6)](SO4)(2), where X = H or D, are reported. This study is concerned with the origin of the structural phase change that is known to occur upon deuteration. Data for the deuterated salt were measured in the metastable state, achieved by application of 500 bar of hydrostatic pressure at similar to303 K followed by cooling to 281 K and the subsequent release of pressure. This allows for the direct comparison between the hydrogenous and deuterated salts, in the same modification, at ambient pressure and low temperature. The Raman spectra provide no intimation of any significant change in the intermolecular bonding. Furthermore, structural differences are few, the largest being for the long Cu-O bond, which is 2.2834(5) and 2.2802(4) Angstrom for the hydrogenous and the deuterated salts, respectively. Calorimetric data for the deuterated salt are also presented, providing an estimate of 0.17(2) kJ/mol for the enthalpy difference between the two structural forms at 295.8(5) K. The structural data suggest that substitution of hydrogen for deuterium gives rise to changes in the hydrogen-bonding interactions that result in a slightly reduced force field about the copper(II) center. The small structural differences suggest different relative stabilities for the hydrogenous and deuterated salts, which may be sufficient to stabilize the hydrogenous salt in the anomalous structural form.