Integrability of a t - J model with impurities

A t - J model for correlated electrons with impurities is proposed. The impurities are introduced in such a way that integrability of the model in one dimension is not violated. The algebraic Bethe ansatz solution of the model is also given and it is shown that the Bethe states are highest weight states with respect to the supersymmetry algebra gl(2/1).

Quasispin graded-fermion formalism and gl(m vertical bar n)down arrow osp(m vertical bar n) branching rules

The graded-fermion algebra and quasispin formalism are introduced and applied to obtain the gl(m\n)down arrow osp(m\n) branching rules for the two- column tensor irreducible representations of gl(m\n), for the case m less than or equal to n(n > 2). In the case m < n, all such irreducible representations of gl(m\n) are shown to be completely reducible as representations of osp(m\n). This is also shown to be true for the case m=n, except for the spin-singlet representations, which contain an indecomposable representation of osp(m\n) with composition length 3. These branching rules are given in fully explicit form. (C) 1999 American Institute of Physics. [S0022-2488(99)04410-2].

Maximal sets of Hamilton cycles in Kn,n

In this article, we prove that there exists a maximal set of m Hamilton cycles in K-n,K-n if and only if n/4 < m less than or equal to n/2. (C) 2000 John Wiley & Sons, Inc.

Conformations of cyclic octapeptides and the influence of heterocyclic ring constraints upon calcium binding

A comparison is made between the structures and calcium binding properties of four cyclic octapeptides that differ in the number of heterocyclic thiazole and oxazoline ring constraints. The conformations of the naturally occurring cyclic octapeptides ascidiacyclamide 1 and patellamide D 2, which each contain two oxazoline and two thiazole rings, are compared by H-1 NMR spectroscopy with the analogues cyclo(Thr-D-Val(Thz)-Ile)(2) 3 with just two thiazoles, and cyclo(Thr-D-Val-alpha Abu-Ile)(2) 4, with no 5-membered rings. The conformations observed in the solid state for ascidiacyclamide (saddle) and patellamide D (twisted figure of eight) were retained in solution, whilst peptide 3 was found to have a chair shape and peptide 4 displayed a range of conformations. The solid state structure of 4 revealed that the peptide takes a relatively planar conformation with a number of transannular hydrogen bonds, which are apparently retained in solution. Complexation studies utilising H-1 NMR and CD spectroscopy yielded 1∶1 calcium-peptide binding constants (log K) for the four peptides (2.9 (1), 2.8 (2), 4.0 (3) and 5.5 (4)) as well as a 1 : 2 metal-peptide binding constant for 3 (log K = 4.5). The affinity for Ca2+ thus decreases with increasing number of 5-membered ring constraints in the macrocycle (4 > 3 > 2 approximate to 1).

Solution of a two-leg spin ladder system

A model for a spin-1/2 ladder system with two legs is introduced. It is demonstrated that this model is solvable via the Bethe ansatz method for arbitrary values of the rung coupling J. This is achieved by a suitable mapping from the Hubbard model with appropriate twisted boundary conditions. We determine that a phase transition between gapped and gapless spin excitations occurs at the critical value J(c) = 1/2 of the rung coupling.

Cyclic octapeptides containing thiazole. Effect of stereochemistry and degree of flexibility on calcium binding properties

Solution conformation and calcium binding properties have been investigated for the two cyclic octapeptides cyclo(-D-Thr-D-Val(Thz)-Ile-)(2) (4) and cyclo(-Thr-Gly(Thz)-Ile-Ser-Gly(Thz)-Ile-)(5) and the results are compared to those for the cyclic octapeptides previously studied; ascidiacyclamide (1), patellamide D (2), cyclo(-Thr-D-Val(Thz)-Ile-)(2) (3), and cyclo(-Thr-D-Val-alphaAbu-Ile-)2 (6). Both 4 and 5 contain two heterocyclic thiazole ring constraints but the latter has a larger degree of flexibility as a consequence of the glycine residues within the cyclic framework. The solution conformation of 4 and 5 was determined from H-1 NMR spectra and found to be a twisted figure of eight similar to that for 2. Complexation studies using H-1 NMR and CD spectroscopy yielded 1 : 1 calcium-peptide binding constants (logK) for the two peptides (2.3 (4) and 5.7 (5)). For 5 the magnitude of the binding constant was verified by a competition titration using CD. The different calcium-binding affinities of 3 (logK = 4.0) and 4 is attributed to the stereochemistry of the threonine residue. The magnitude of the binding constant for 5 compared to 3 and 4 (all peptides containing two thiazole ring constrains) demonstrates that the increase in flexibility of the cyclic peptide has a dramatic effect on the Ca2+ binding ability. The affinity for Ca2+ thus decreases in the order (6 similar to 5 > 3 > 2 similar to 1 > 4). The number of carbonyl donors available on each peptide has only a limited effect on calcium binding. The most important factor is the flexibility, which allows for a conformation of the peptide capable of binding calcium efficiently.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Algebraic Bethe ansatz for the anisotropic supersymmetric U model

We present an algebraic Bethe ansatz for the anisotropic supersymmetric U model for correlated electrons on the unrestricted 4(L)-dimensional electronic Hilbert space x(n=l)(L)C(4)(where L is the lattice length). The supersymmetry algebra of the local Hamiltonian is the quantum superalgebra U-q[gl(2\1)] and the model contains two symmetry-preserving free real parameters; the quantization parameter q and the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of U-q[gl(2\1)]. Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice.

Quantum Lie algebras, their existence, uniqueness and q-antisymmetry

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules L-h(g) of the quantized enveloping algebras U-h(g). On them the quantum Lie product is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie algebra g(h) independent of any concrete realization. Its h-dependent structure constants are given in terms of inverse quantum Clebsch-Gordan coefficients. We then show that all concrete quantum Lie algebras L-h(g) are isomorphic to an abstract quantum Lie algebra g(h). In this way we prove two important properties of quantum Lie algebras: 1) all quantum Lie algebras L-h(g) associated to the same g are isomorphic, 2) the quantum Lie product of any Ch(B) is q-antisymmetric. We also describe a construction of L-h(g) which establishes their existence.

Alternatives for parallel Krylov subspace basis computation

Numerical methods related to Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated via their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. However, although easily parallelizable, this technique is not as scalable as expected for communications. In this work we examine alternative methods aimed at overcoming this drawback. Since they retrieve upon completion the same information as Arnoldi's algorithm does, they enable us to design a wide family of stable and scalable Krylov approximation methods for various parallel environments. We present timing results obtained from their implementation on two distributed-memory multiprocessor supercomputers: the Intel Paragon and the IBM Scalable POWERparallel SP2. (C) 1997 by John Wiley & Sons, Ltd.

Casimir invariants and characteristic identities for gl(infinity)

A full set of (higher-order) Casimir invariants for the Lie algebra gl(infinity) is constructed and shown to be well defined in the category O-FS generated by the highest weight (unitarizable) irreducible representations with only a finite number of nonzero weight components. Moreover, the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(infinity) are also determined and generalize those previously obtained for gl(n) by Bracken and Green [A. J. Bracken and H. S. Green, J. Math. Phys. 12, 2099 (1971); H. S. Green, ibid. 12, 2106 (1971)]. (C) 1997 American Institute of Physics.

Exact solution for the Bariev model with boundary fields

The Bariev model with open boundary conditions is introduced and analysed in detail in the framework of the Quantum Inverse Scattering Method. Two classes of independent boundary reflecting K-matrices leading to four different types of boundary fields are obtained by solving the reflection equations. The models are exactly solved by means of the algebraic nested Bethe ansatz method and the four sets or Bethe ansatz equations as well as their corresponding energy expressions are derived. (C) 2001 Elsevier Science B.V. All rights reserved.

Integrable open boundary conditions for the Bariev model of three coupled X Y spin chains

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique and the Bethe ansatz equations are derived. (C) 2001 Elsevier Science B.V. All rights reserved.