Exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions

We study the exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions. The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method. Based on the off-diagonal Bethe ansatz solutions, we construct the Bethe states of the inhomogeneous X X X Heisenberg spin chain with the generic open boundaries. By taking a quasi-classical limit, we give explicit closed-form expression of the Bethe states of the Gaudin model. From the numerical simulations for the small-size system, it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1) symmetry. Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant. This fact enables us to recover the Bethe states of the Gaudin model with the U(1) symmetry. These results provide a basis for the further study of the thermodynamic limit, correlation functions, and quantum dynamics of the Gaudin model.     

Two magnetic impurities with arbitrary spins in open boundary t-J model

From the open boundary t-J model an impurity model is constructed in which magnetic impurities of arbitrary spins are coupled to the edges of the strongly correlated electron system. The boundary R matrices are given explicitly. The interaction parameters between magnetic impurities and electrons are related to the potentials of the impurities to preserve the integrability of the system. The Hamiltonian of the impurity model is diagonalized exactly. The integral equations of the ground state are derived and the ground state properties are discussed in detail. We discuss also the string solutions of the Bethe ansatz equations, which describe the bound states of the charges and spins. By minimizing the thermodynamic potential we get the thermodynamic Bethe ansatz equations. The finite size correction of the free energy contributed by the magnetic impurities is obtained explicitly. The properties of the system at some special limits are discussed and the boundary bound states are obtained.     

Airy Functions in the Thermodynamic Bethe Ansatz

Thermodynamic Bethe ansatz equations are coupled nonlinear integral equations which appear frequently when solving integrable models. Those associated with models with N=2 supersymmetry can be related to differential equations, among them Painlevé III and the Toda hierarchy. In the simplest such case, the massless limit of these nonlinear integral equations can be solved in terms of the Airy function. This is the only known closed-form solution of thermodynamic Bethe ansatz equations, outside of free or classical models. This turns out to give the spectral determinant of the Schrödinger equation in a linear potential.     

Exact solution of the general non-intersecting string model

We present a thorough analysis of the non-intersecting string (NIS) model and its exact solution. This is an integrable q-states vertex model describing configurations of non-intersecting polygons on the lattice. The exact eigenvalues of the transfer matrix are found by the analytic Bethe ansatz. The Bethe ansatz equations thus found are shown to be equivalent to those for a mixed spin model involving both and infinite spin. This indicates that the NIS model provides a representation of the quantum group corresponding to spins and s = ∞. The partition function and the excitations in the thermodynamic limit are computed.     

Exact excitation spectrum of the Zn + 1 × Zn + 1 generalized Heisenberg model

We describe the excitations of the generalization of the Heisenberg anisotropic hamiltonian to Z_{n + 1} spins. We analyse the Bethe ansatz equations without assuming the existence of strings. Excited states above an antiferromagnetic ground state are described by a finite number of parameters, which verify system of equations. We give the energy and momentum of the excitations. In a suitable limit we recover the spectrum of a relativistically invariant theory.     

Thermodynamics of 1D N-Component Bariev Model Under Open Boundary Conditions

The thermodynamic Bethe ansatz equations and free energy for 1D N-component Bariev model under open boundary conditions are derived based on the string hypothesis for both, a repulsive and an attractive interaction. These equations are discussed in some limiting cases, such as the ground state, weak and strong couplings.     

Thermodynamics of 1D N-Component Bariev Model Under Open Boundary Conditions

The thermodynamic Bethe ansatz equations and free energy for 1D N-component Bariev model under open boundary conditions are derived based on the string hypothesis for both, a repulsive and an attractive interaction.These equations are discussed in some limiting cases, such as the ground state, weak and strong couplings.     

Probability distributions of line lattices in random media from the 1D Bose gas

The statistical properties of a two-dimensional lattice of elastic lines in a random medium are studied using the Bethe ansatz. We present a novel mapping of the dilute random line lattice onto the weak coupling limit of a pure Bose gas with delta-function interactions. Using this mapping, we calculate the cumulants of the free energy in the dilute limit exactly. The relation between density and displacement correlation functions in the two models is examined and compared with existing results from renormalization group and variational ansätze.     

Integrability of N-Component Bariev Model Under Open Boundary Conditions

N-component Bariev model for correlated hopping under open boundary conditions in one dimension is studied in the framework of Bethe ansatz method. The energy spectrum and the related Bethe ansatz equations are obtained.     

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.     

Exact Solutions of One-Dimensional N-Component Bariev Model with General Boundary Conditions

The N-component Bariev model for correlated hopping with open boundary conditions in one dimension is studied in the framework of coordinate Bethe ansatz method. The energy spectrum, integrable boundary conditions and the corresponding Bethe ansatz equations are derived.     

Exact Solutions of One-Dimensional N-Component Bariev Model with General Boundary Conditions

The N-component Bariev model for correlated hopping with open boundary conditions in one dimension is studied in the framework of coordinate Bethe ansatz method. The energy spectrum, integrable boundary conditions and the corresponding Bethe ansatz equations are derived.     

Bethe ansatz equations for the brokenZ N -symmetric model

We obtain the Bethe ansatz equations for the brokenZ _N -symmetric model by constructing a functional relation of the transfer matrix ofL-operators. This model is an elliptic off-critical extension of the Fateev-Zamolodchikov model. We calculate the free energy of this model on the basis of the string hypothesis.     

Bethe ansatz for the XXX-S chain with non-diagonal open boundaries

We consider the algebraic Bethe ansatz solution of the integrable and isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show that the corresponding K-matrices are similar to diagonal matrices with the help of suitable transformations independent of the spectral parameter. When the boundary parameters satisfy certain constraints we are able to formulate the diagonalization of the associated double-row transfer matrix by means of the quantum inverse scattering method. This allows us to derive explicit expressions for the eigenvalues and the corresponding Bethe ansatz equations. We also present evidences that the eigenvectors can be build up in terms of multiparticle states for arbitrary S.     

Analysis of the Bethe ansatz equations of the XXZ model

We analyse the Bethe ansatz equations of the XXZ model in the antiferromagnetic region, without assuming a priori the existence of strings. Excited states are described by a finite number of parameters. These parameters satisfy a closed system of equations, which we obtain by eliminating the parameters of the vacuum from the original Bethe ansatz equations. Strings are only particular solutions of these equations.     

Exact Solution of the One-Dimensional N-Component Bariev Model with a Hard-Core Repulsion under Open Boundary Conditions

We analyse the integrable boundary conditions for the one-dimensional N-component generalized Bariev model with a hard-core repulsion. The Bethe ansatz equations and the energy spectrum are obtained in the framework of the nested Bethe ansatz method.     

开边界条件下一类新Hubbard模型的精确解

用坐标Bethe ansatz方法详细研究了开边界条件下一类新Hubbard模型的可积性问题. 得到了系统的能谱、可积边界条件和Bethe ansatz方程.     

Algebraic Bethe ansatz for the gl(1|2) generalized model and Lieb–Wu equations

We solve the gl(1|2) generalized model by means of the algebraic Bethe ansatz. The resulting eigenvalue of the transfer matrix and the Bethe ansatz equations depend on three complex functions, called the parameters of the generalized model. Specifying the parameters appropriately, we obtain the Bethe ansatz equations of the supersymmetric t-J model, the Hubbard model, or of Yang's model of electrons with delta interaction. This means that the Bethe ansatz equations of these (and many other) models can be obtained from a common algebraic source, namely from the Yang–Baxter algebra generated by the gl(1|2) invariant R-matrix.     

Integrable open boundary conditions for the Bariev model of three coupled XY 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.     

Separation of variables for integrable spin–boson models

We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang–Baxter algebra. The main deviation from the standard approach consists in a half infinite Sklyanin lattice made of the eigenvalues of the operator zeros of the Bethe annihilation operator. By a separation of variables, functional TQ-equations are obtained for this half infinite lattice. They provide valuable information about the spectrum of a given Hamiltonian model. We apply this procedure to integrable spin–boson models subject to both twisted and open boundary conditions. In the case of general twisted and certain open boundary conditions polynomial solutions to these TQ-equations are found and we compute the spectrum of both the full transfer matrix and its quasi-classical limit. For generic open boundaries we present a two-parameter family of Bethe equations, derived from TQ-equations that are compatible with polynomial solutions for Q. A connection of these parameters to the boundary fields is still missing.