Phase diagram of the one-dimensional Holstein model of spinless fermions

The one-dimensional Holstein model of spinless fermions interacting with dispersionless phonons is studied using a new variant of the density matrix renormalization group. By examining various low-energy excitations of finite chains, the metal-insulator phase boundary is determined precisely and agrees with the predictions of strong coupling theory in the antiadiabatic regime and is consistent with renormalization group arguments in the adiabatic regime. The Luttinger liquid parameters, determined by finite-size scaling, are consistent with a Kosterlitz-Thouless transition.

Phase diagram for a class of spin-1/2 Heisenberg models interpolating between the square-lattice, the triangular-lattice, and the linear-chain limits

We study the spin-1/2 Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square lattice at one end, a set of decoupled spin chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations, and varying dimensionality. There is a large region of the usual two-sublattice Neel phase, a three-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wave vector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical. [S0163-1829(99)10421-1].

Phase diagram of a Heisenberg spin-Peierls model with quantum phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

Experimental characterization of continuous-variable entanglement

We present an experimental analysis of quadrature entanglement produced from a pair of amplitude squeezed beams. The correlation matrix of the state is characterized within a set of reasonable assumptions, and the strength of the entanglement is gauged using measures of the degree of inseparability and the degree of Einstein-Podolsky-Rosen (EPR) paradox. We introduce controlled decoherence in the form of optical loss to the entangled state, and demonstrate qualitative differences in the response of the degrees of inseparability and EPR paradox to this loss. The entanglement is represented on a photon number diagram that provides an intuitive and physically relevant description of the state. We calculate efficacy contours for several quantum information protocols on this diagram, and use them to predict the effectiveness of our entanglement in those protocols.

Continuous quantum error correction by cooling

We describe an implementation of quantum error correction that operates continuously in time and requires no active interventions such as measurements or gates. The mechanism for carrying away the entropy introduced by errors is a cooling procedure. We evaluate the effectiveness of the scheme by simulation, and remark on its connections to some recently proposed error prevention procedures.

Phase diagram of the three-band half-filled Cu-O two-leg ladder

We determine the phase diagram of the half-filled two-leg ladder both at weak and strong coupling, taking into account the Cu d(x)(2)-y(2) and the O p(x) and p(y) orbitals. At weak coupling, renormalization group flows are interpreted with the use of bosonization. Two different models with and without outer oxygen orbitals are examined. For physical parameters, and in the absence of the outer oxygen orbitals, the D-Mott phase arises; a dimerized phase appears when the outer oxygen atoms are included. We show that the circulating current phase that preserves translational symmetry does not appear at weak coupling. In the opposite strong-coupling atomic limit the model is purely electrostatic and the ground states may be found by simple energy minimization. The phase diagram so obtained is compared to the weak-coupling one.

Movement and figurality: The circulation diagram and the history of the architectural plan

Knowledge of the plan competes with self-consciousness of experience. The less we are able to understand our spatio-visual experience by the abstract coordinates of the plan, the more we are thrust back into a lived experience of the building in duration. This formula, frequently unacknowledged, has been one of the main precepts of the experientialist modernism which arises out of the picturesque and which stands in critique of classical idealism. One of the paths to critique this formula is by showing that the attention to the experience of the spaces in duration is predicated on obscuring, complicating and weakening the apprehension of the plan as a figure. Another development in the practice of modern planning has been architects using a kind of over-drawing where human circulation diagrams or 'movement lines' are drawn expressively across the orthographic plane; thus representing the lived experience of buildings. We will show that these two issues are linked; the plan's weak figure and the privilege this supposes for durational experience has a corollary - experience itself demands to be visible in the plan, and this is one origin of the present fascination with 'diagramming'. In this paper we explore the practice of architectural planning and its theoretical underpinnings in an attempt to show the viability of a history of architectural planning methods.

Synthesis of silica films at the air/water interface: Effect of template chain length and ionic strength

We have grown surfactant-templated silicate films at the air-water interface using n-alkyltrimethylammonium bromide and chloride in an acid synthesis with tetraethyl orthosilicate as the silicate source. The films have been grown with and without added salt (sodium chloride, sodium bromide) and with n-alkyl chain lengths from 12 to 18, the growth process being monitored by X-ray reflectometry. Glassy, hexagonal, and lamellar structures have been produced in ways that are predictable from the pure surfactant-water phase diagrams. The synthesis appears to proceed initially through an induction period characterized by the accumulation of silica-coated spherical micelles near the surface. All syntheses, except those involving C(12)TACl, show a sudden transformation of the spherical micellar phase to a hexagonal phase. This occurs when the gradually increasing ionic strength and/or changing ethanol concentration is sufficient to change the position of boundaries within the phase diagram. A possible mechanism for this to occur may be to induce a sphere to rod transition in the micellar structure. This transformation, as predicted from the surfactant-water phase diagram, can be induced by addition of salts and is slower for chloride than bromide counteranions. The hexagonal materials change in cell dimension as the chain length is changed in a way consistent with theoretical model predictions. All the materials have sufficiently flexible silica frameworks that phase interconversion is observed both from glassy to hexagonal and from hexagonal, to lamellar and vice versa in those surfactant systems where multiple phases are found to exist.

The mechanisms of combustion and continuous reactions during mechanical alloying

Some materials exhibit a combustion event during mechanical alloying, which results in the rapid transformation of reactants into products, while others show a slow transformation of reactants into products, In this paper, the continuous W + C --> WC reaction is compared to the Ti + C --> TiC combustion reaction. Rietveld refinement of X-ray diffraction patterns is used to show that these particular reactions proceed through different pathways, determined by crystallographic factors of the reactants. When a crystallographic relationship exists between the reactants and the products, such as that between W and WC, the product forms slowly over a period of time. In contrast, insertion of C into the Ti structure is associated with atomic rearrangements within the crowded lattice planes and the subsequent catastrophic failure of the reactant lattices results in combustion to form TiC. (C) 2001 Academic Press.