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.     

On Nested Bethe Ansatz for RTT Algebra of o(2n) Type

We study the highest weight representations of the RTT algebras for the R matrix of o(2n) type by the nested algebraic Bethe ansatz. We show how auxiliary RTT algebra à can be used to find Bethe vectors and Bethe conditions. For special representations, in which representation of RTT algebra à is trivial, the problem was solved by Reshetikhin.

     

Algebraic properties of an integrable t-J model with impurities

We investigate the algebraic structure of a recently proposed integrable t-J model with impurities. Three forms of the Bethe ansatz equations are presented corresponding to the three choices for the grading. We prove that the Bethe ansatz states are highest weight vectors of the underlying gl(2′1) supersymmetry algebra. By acting with the gl(2′1) generators we construct a complete set of states for the model.     

Colored Quantum Algebra and Its Bethe State

We investigate the colored Yang-Baxter equation. Based on a trigonometric solution of colored Yang-Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.     

Exact solutions of graded Temperley-Lieb Hamiltonians

Orthosymplectic Hamiltonians derived from representations of the graded Temperley-Lieb algebra are presented and solved via the coordinate Bethe ansatz. The spectra of these Hamiltonians are obtained using open and closed boundary conditions.     

U(1) symmetry in the current algebra and N-fermionic massless Thirring model

Local U(1) symmetry in current algebra constructed by fermions has been found. The symmetry is related to the simplest q-deformation of N-fermions. We give the physical interpretation through the N-fermionic massless Thirring model. The Bethe ansatz wavefunction is also given.     

Application of Nonlinear Lie Algebraic Method to One-Dimensional spin-1/2 Heisenberg Ferromagnetic Chain

In our work the nonlinear Lie algebra and concept of shift operator are introduced, based on that the eigenproblern of one-dimensional spin-1/2 Heisenberg ferromagnetic chain can be solved. The results achieved from the usual Bethe ansatz method are recovered naturally.     

Orthofermions versus Gutzwiller projection operator approach for the infinite U Hubbard model

A comparison of two well-known approaches for strongly correlated electron systems, namely, nested Bethe ansatz implemented through orthofermion algebra and Gutzwiller projection operator formalism, is made by calculating the energy spectrum of 1D infinite U Hubbard model for a finite system consisting of three particles on a four site anisotropic closed chain. It is shown that orthofermion algebra always leads to at least an eight hold degeneracy in the energy spectrum corresponding to all 2³ spin configurations, consistent with the nested Bethe ansatz solution leading to a N²-fold degeneracy of energy levels of an N electron system. Such a degeneracy is absent in the Gutzwiller projection operator approach. This finding shows the limitations of the Gutzwiller projection method and at the same time the relevance of orthofermion approach for the infinite U Hubbard model.     

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.     

Solutions to Braid Group,Yang-Baxter Equation and Integrable Fermion Systems

Braid group representations are found in ferrnion systems in one space dimension. Explicit baxterization is performed to find corresponding new trigonometric solu tions of Yang-Baxter equation. The quantum algebra structures implied in the new solutions are discovered. Algebraic Bethe ansatz method is applied to solving these systems. The relationships between these fermion systems and polaron model, spin-1/2 Heisenberg spin chain are discussed.     

Integrability of a New Type of Deformed XXZ Model

A new type of deformed XXZ model was constructed and diagonalized by the coordinate Bethe ansatz method. We obtained the energy and the Bethe ansatz equations of the model and also discussed some thermodynamics of the model.     

Exactly Solved Fermion-Boson Model for Heavy-Fermion Alloys

The exact eigenstates of the Hamiltonian of the fermion-boson model for heavy-fermion alloys are constructed by using the Bethe ansatz. The Bethe ansatz equations are obtained from the periodic boundary conditions.     

Dirac Equation and Some Quasi-Exact Solvable Potentials in the Turbiner’s Classification

In this paper quasi-exact solvability (QES) of Dirac equation with some scalar potentials based on sl(2) Lie algebra is studied. According to the quasi-exact solvability theory, we construct the configuration of the classes II, IV, V, and X potentials in the Turbiner's classification such that the Dirac equation with scalar potential is quasi-exactly solved and the Bethe ansatz equations are derived in order to obtain the energy eigenvalues and eigenfunctions.     

The exact solution and the finite-size behaviour of the Osp(1|2)-invariant spin chain

We have solved exactly the Osp(1|2) spin chain by the Bethe ansatz approach. Our solution is based on an equivalence between the Osp(1|2) chain and a certain special limit of the Izergin-Korepin vertex model. The completeness of the Bethe ansatz equations is discussed for a system with four sites and the appearance of special string structures is noted. The Bethe ansatz presents an important phase factor which distinguishes the even and odd sectors of the theory. The finite-size properties are governed by a conformal field theory with central charge c = 1.     

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.     

Bethe ansatz for an open Heisenberg spin chain with impurity

We have set up the algebraic Bethe ansatz equation for an open Heisenberg spin chain having an impurity of a different type of spin. The chain is considered to be open and hence the QISM approach as modified by Sklyanin is used to set up the equations for the Bethe ansatz.     

Extending the Bethe Ansatz: The Quantum Three-Particle Ring

The quantum problem of three impenetrable particles of arbitrary mass confined to a ring is solved by the Bethe ansatz. The solution of this problem is intimately related to the solution a Helmholtz equation in the interior of an arbitrary acute triangle, a problem thought insoluble by Bethe ansatz methods.     

SOLVABLE BOSON-FERMION MODEL FOR MIXED-VALENCE SYSTEMS

Using the Bethe ansatz technique, the exact eigenstates of the Hamiltonian of the boson-fermion model for mixed-valence systems are constructed. The Bethe ansatz equations are obtained from the periodic boundary conditions.     

sl玻色子体系在U(2l+1)O(2l+2)过渡区的严格解

利用无穷维李代数方法得到了相互作用sl玻色子体系在U( 2l+ 1 ) O( 2l+ 2 )过渡区的能谱和波函数的严格解 .给出了该系统Bethe假定方程的数值解法 .     

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.