Exact surface energy and elementary excitations of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields

We study the physical properties of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields. By using a combination of numerical analysis and analytical method, we obtain the surface energy and elementary excitations of the model. It shows that the contributions of the two boundary fields to the surface energy are additive. We also find that there exists a kind of excitations related to the boundary string.

Drinfeld Twist and Symmetric Bethe Vectors of Open XYZ Chain with Non-Diagonal Boundary Terms

With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex solid-on-solid(SOS) model,we find that in the F-basis provided by the twist the two sets of pseudo-particle creation operators simultaneously take completely symmetric and polarization free form.This allows us to obtain the explicit and completely symmetric expressions of the two sets of Bethe states of the model.

一维Heisenberg格子磁性链:代数Bethe-Ansatz方程

本文研究一维Heisenberg格子磁性链的量子完全可积性.通过求解杨-Baxter方程,得到了量子R矩阵,进而构造了此模型的代数Bethe-Ansatz方程.

Second Reference State and Complete Eigenstates of Open XYZ Chain

The second reference state of the open XYZ spin chain with non-diagonal boundary terms is studied. The associated Bethe states exactly yield the second set of eigenvalues proposed recently by functional Bethe Ansatz.

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.

Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

The U(1)symmetry of the X X Z central spin model with an arbitrary central magnetic field B is broken,since its total spin in the z-direction is not conserved.We obtain the exact solutions of the system by using the off-diagonal Bethe ansatz method.The thermodynamic limit is investigated based on the solutions.We find that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy satisfies an N^(-1)scaling law,where N is the total number of spins.This result makes it possible to investigate the properties of the system in the thermodynamic limit.By assuming the structural form of the Bethe roots in the thermodynamic limit,we obtain the contribution of the direction of B to the ground state energy.It is shown that the contribution of the direction of the central magnetic field is a finite value in the thermodynamic limit.This is the phenomenon caused by the U(1)symmetry breaking of the system.

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.

Lax pair formulation for the open boundary Osp(1|2)spin chain

Based on the Lax pair formulation,we study the integrable conditions of the Osp(1|2)spin chain with open boundaries.We consider both the non-graded and graded versions of the Osp(1|2)chain.The Lax pair operators M_(±)for the boundaries can be induced by the Lax operator M_(j)for the bulk of the system.They correspond to the reflection equations(RE)and the Yang-Baxter equation,respectively.We further calculate the boundary K-matrices for both the non-graded and graded versions of the model with open boundaries.The double row monodromy matrix and transfer matrix of the spin chain have also been constructed.The K-matrices obtained from the Lax pair formulation are consistent with those from Sklyanin’s RE.This construction is another way to prove the quantum integrability of the Osp(1|2)chain.We find that the Lax pair formulation has advantages in dealing with the boundary terms of the supersymmetric model.

Exact solution of an anisotropic J_(1)–J_(2)model with the Dzyloshinsky–Moriya interactions at boundaries

We propose a method to construct new quantum integrable models.As an example,we construct an integrable anisotropic quantum spin chain which includes the nearest-neighbor,next-nearestneighbor and chiral three-spin couplings.It is shown that the boundary fields can enhance the anisotropy of the first and last bonds,and can induce the Dzyloshinsky–Moriya interactions along the z-direction at the boundaries.By using the algebraic Bethe ansatz,we obtain the exact solution of the system.The energy spectrum of the system and the associated Bethe ansatz equations are given explicitly.The method provided in this paper is universal and can be applied to constructing other exactly solvable models with certain interesting interactions.