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.

Integrable multiparametric quantum spin chains

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions, We illustrate how this general formalism applier; to construct multiparametric versions of the supersymmetric t-J and Li models.

An open-boundary integrable model of three coupled XY spin chains

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms is determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived. (C) 1998 Elsevier Science B.V.

On the construction of integrable closed chains with quantum supersymmetry

We present a general prescription for the construction of integrable one-dimensional systems with closed boundary conditions and quantum supersymmetry.

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].

Measurement-based teleportation along quantum spin chains

We examine the teleportation of an unknown spin-1/2 quantum state along a quantum spin chain with an even number of sites. Our protocol, using a sequence of Bell measurements, may be viewed as an iterated version of the 2-qubit protocol of C. H. Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)]. A decomposition of the Hilbert space of the spin chain into 4 vector spaces, called Bell subspaces, is given. It is established that any state from a Bell subspace may be used as a channel to perform unit fidelity teleportation. The space of all spin-0 many-body states, which includes the ground states of many known antiferromagnetic systems, belongs to a common Bell subspace. A channel-dependent teleportation parameter O is introduced, and a bound on the teleportation fidelity is given in terms of O.

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 generalized spin ladder models based on the SU(1|3) and SU(3|1) algebras

We present two integrable spin ladder models which possess a general free parameter besides the rung coupling J. The models are exactly solvable by means of the Bethe ansatz method and we present the Bethe ansatz equations. We analyze the elementary excitations of the models which reveal the existence of a gap for both models that depends on the free parameter. (C) 2003 American Institute of Physics.

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.

Algebraic Bethe ansatz for integrable one-dimensional extended Hubbard models with open boundary conditions

Nine classes of integrable open boundary conditions, further extending the one-dimensional U-q (gl (212)) extended Hubbard model, have been constructed previously by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary systems are now solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained for all nine cases.

Integrable anisotropic spin-ladder model

We present an integrable spin-ladder model, which possesses a free parameter besides the rung coupling J. Wang's system based on the SU(4) symmetry can be obtained as a special case. The model is exactly solvable by means of the Bethe ansatz method. We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram. Finally, we show that the model is a special case of a more general Hamiltonian with three free parameters.

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].

Non-diagonal solutions of the reflection equation for the trigonometric A((1)) (n-1) vertex model

We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric A(n-1)((1)) vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric R-matrices. In addition to a discrete (positive integer) parameter l, 1 less than or equal to l less than or equal to n, the solution contains n + 2 continuous boundary parameters.

Izergin-Korepin model with a boundary

The Izergin-Korepin model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the twisted quantum affine algebra U-q[((2))(2)]. We give the bosonization of the vacuum state with zero particle content. Excitation states are given by the action of the vertex operators on the vacuum state. We derive the boundary S-matrix. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy. (C) 2001 Elsevier Science B.V. All rights reserved.

A(n-1) Gaudin model with open boundaries

The A(n-1) Gaudin model with integrable boundaries specified by non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained. (c) 2005 Elsevier B.V. All rights reserved.