Yang-Baxter Equations With Reflection Associated With the Scattering From Kaleidoscope

YBE associated with the scattering from kaleidoscopes of Sutherland has been found. The reflection behaviour at the Dynkin diagram and its physical meaning are explored.

Exact solution of Heisenberg model with site-dependent exchange couplings and Dzyloshinsky–Moriya interaction

We propose an integrable spin-1/2 Heisenberg model where the exchange couplings and Dzyloshinky-Moriya interactions are dependent on the sites. By employing the quantum inverse scattering method, we obtain the eigenvalues and the Bethe ansatz equation of the system with the periodic boundary condition. Furthermore, we obtain the exact solution and study the boundary effect of the system with the anti-periodic boundary condition via the off-diagonal Bethe ansatz. The operator identities of the transfer matrix at the inhomogeneous points are proved at the operator level. We construct the T -Q relation based on them. From which, we obtain the energy spectrum of the system. The corresponding eigenstates are also constructed. We find an interesting coherence state that is induced by the topological boundary.

Exact solution of an integrable quantum spin chain with competing interactions

We construct an integrable quantum spin chain that includes the nearest-neighbor,next-nearest-neighbor,chiral threespin couplings,Dzyloshinsky–Moriya interactions and unparallel boundary magnetic fields.Although the interactions in bulk materials are isotropic,the spins nearby the boundary fields are polarized,which induce the anisotropic exchanging interactions of the first and last bonds.The U(1)symmetry of the system is broken because of the off-diagonal boundary reflections.Using the off-diagonal Bethe ansatz,we obtain an exact solution to the system.The inhomogeneous T–Q relation and Bethe ansatz equations are given explicitly.We also calculate the ground state energy.The method given in this paper provides a general way to construct new integrable models with certain interesting interactions.

Off-diagonal approach to the exact solution of quantum integrable systems

We investigate the t–W scheme for the anti-ferromagnetic X X X spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of the transfer matrix. Based on it, we obtain the exact solution of the system. By analyzing the distribution of zero roots at the ground state, we obtain the explicit expressions of the eigenfunctions of the transfer matrix and the associated W operator(see Eqs.(10) and(70)) in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of W operator for the ground state exhibits exponential decay behavior. Thus this fact ensures that the so-called inversion relation(the t–W relation without the W-term) can be used to study the ground state properties of quantum integrable systems with/without U(1)-symmetry in the thermodynamic limit.

Integrable boundary conditions for the B2 model

New integrable B2 model with off-diagonal boundary reflections is proposed.The general solutions of the reflection matrix for the B2 model are obtained by using the fusion technique.Wefind that the reflection matrix has 7 free boundary parameters,which are used to describe the degree of freedom of boundary couplings,without breaking the integrability of the system.The new quantization conditions will induce the novel structure of the energy spectrum and the boundary states.The corresponding boundary effects can be studied based on the results in this paper.Meanwhile,the reflection matrix of high rank models associated with Bnalgebra can also be obtained by using the method suggested in this paper.