Arbitrary Boundary Fields Research Articles

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.

Exact surface energy and helical spinons in the XXZ spin chain with arbitrary nondiagonal boundary fields

An analytic method is proposed to compute the surface energy and elementary excitations of the XXZ spin chain with generic non-diagonal boundary fields. For the gapped case, in some boundary parameter regimes the contributions of the two boundary fields to the surface energy are non-additive. Such a correlation effect between the two boundaries also depends on the parity of the site number $N$ even in the thermodynamic limit $N\to\infty$. For the gapless case, contributions of the two boundary fields to the surface energy are additive due to the absence of long-range correlation in the bulk. Although the $U(1)$ symmetry of the system is broken, exact spinon-like excitations, which obviously do not carry spin-$\frac12$, are observed. The present method provides an universal procedure to deal with quantum integrable systems either with or without $U(1)$ symmetry.

Inhomogeneous matrix product ansatz and exact steady states of boundary-driven spin chains at large dissipation.

We find novel site-dependent Lax operators in terms of which we demonstrate exact solvability of a dissipatively driven XYZ spin-1/2 chain in the Zeno limit of strong dissipation, with jump operators polarizing the boundary spins in arbitrary directions. We write the corresponding nonequilibrium steady state using an inhomogeneous matrix product ansatz, where the constituent matrices satisfy a simple set of linear recurrence relations. Although these matrices can be embedded into an infinite-dimensional auxiliary space, we have verified that they cannot be simultaneously put into a tridiagonal form, not even in the case of axially symmetric (XXZ) bulk interactions and general nonlongitudinal boundary dissipation. We expect our results to have further fundamental applications for the construction of nonlocal integrals of motion for the open XYZ model with arbitrary boundary fields, or the eight-vertex model.

Surface energy and elementary excitations of the XXZ spin chain with arbitrary boundary fields

The thermodynamic properties of the XXZ spin chain with integrable open boundary conditions at the gaped region (i.e. the anisotropic parameter being a real number) are investigated. It is shown that the contribution of the inhomogeneous term in the T − Q relation of the ground state and elementary excited state can be neglected when the size of the system N tends to infinity. The surface energy and elementary excitations induced by the unparallel boundary magnetic fields are obtained.

Bethe ansatz solutions of the τ 2-model with arbitrary boundary fields

The quantum $\tau_2$-model with generic site-dependent inhomogeneity and arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix are given in terms of an inhomogeneous T-Q relation, which is based on the operator product identities among the fused transfer matrices and the asymptotic behavior of the transfer matrices. Moreover, the associated Bethe Ansatz equations are also obtained.

Bethe states of the XXZ spin-[formula omitted] chain with arbitrary boundary fields

Based on the inhomogeneous T−Q relation constructed via the off-diagonal Bethe Ansatz, the Bethe-type eigenstates of the XXZ spin-12 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge transformations, proper generators and reference state for constructing Bethe vectors can be obtained respectively. Given an inhomogeneous T−Q relation for an eigenvalue, it is proven that the resulting Bethe state is an eigenstate of the transfer matrix, provided that the parameters of the generators satisfy the associated Bethe Ansatz equations.

Thermodynamic limit and surface energy of the XXZ spin chain with arbitrary boundary fields

In two previous papers [26,27], the exact solutions of the spin-12 chains with arbitrary boundary fields were constructed via the off-diagonal Bethe ansatz (ODBA). Here we introduce a method to approach the thermodynamic limit of those models. The key point is that at a sequence of degenerate points of the crossing parameter η=ηm, the off-diagonal Bethe ansatz equations (BAEs) can be reduced to the conventional ones. This allows us to extrapolate the formulae derived from the reduced BAEs to arbitrary η case with O(N−2) corrections in the thermodynamic limit N→∞. As an example, the surface energy of the XXZ spin chain model with arbitrary boundary magnetic fields is derived exactly. This approach can be generalized to all the ODBA solvable models.

Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields

The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector is constructed. It is shown that the second eigenvalue problem can be transformed into that of the inhomogeneous XXX spin chain with arbitrary boundary fields which can be solved via the off-diagonal Bethe ansatz method.

Off-diagonal Bethe ansatz solutions of the anisotropic spin-[formula omitted] chains with arbitrary boundary fields

The anisotropic spin-12 chains with arbitrary boundary fields are diagonalized with the off-diagonal Bethe ansatz method. Based on the properties of the R-matrix and the K-matrices, an operator product identity of the transfer matrix is constructed at some special points of the spectral parameter. Combining with the asymptotic behavior (for XXZ case) or the quasi-periodicity properties (for XYZ case) of the transfer matrix, the extended T–Q ansatzes and the corresponding Bethe ansatz equations are derived.

Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions

Employing the off-diagonal Bethe ansatz method proposed recently by the present authors, we exactly diagonalize the XXX spin chain with arbitrary boundary fields. By constructing a functional relation between the eigenvalues of the transfer matrix and the quantum determinant, the associated T–Q relation and the Bethe ansatz equations are derived.

TheXXmodel with boundaries: II. Finite-size scaling and partition functions

We compute the continuum limit of the spectra for the XX-model with arbitrary complex boundary fields. In the case of hermitian boundary terms one obtains the partition functions of the free compactified boson field on a cylinder with Neumann-Neumann, Dirichlet-Neumann or Dirichlet-Dirichlet boundary conditions. This applies also for certain non-hermitian boundaries. For special cases we also compute the free surface energy. For certain non-hermitian boundary terms the results are more complex.Here one obtains logarithmic corrections to the free surface energy. The asymmetric version of the XX-model with boundaries (this includes the Dzyaloshinsky-Moriya interaction)is also discussed.