Searcharxiv⌕ Search

arXiv subjects

Kangjie Shi

Publications and source records attributed to Kangjie Shi.

47 records · Page 3Linked to original sources
arXiv2014

Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries

The nested off-diagonal Bethe ansatz method is proposed to diagonalize multi-component integrable models with generic integrable boundaries. As an example, the exact solutions of the su(n)-invariant spin chain model with both periodic and non-diagonal boundaries are derived by constructing the nested T-Q relations based on the operator product identities among the fused transfer matrices and the asymptotic behavior of the transfer matrices.

hep-th↗
arXiv2014

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-1/2 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=η_m, 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 ηcase with O(N^{-2}) corrections in the thermodynamic limit N\to\infty. 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.

cond-mat.stat-mech↗
arXiv2014

Exact solution of the one-dimensional super-symmetric t-J model with unparallel boundary fields

The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are derived for the second eigenvalue problem associated with spin degrees of freedom. It is found that the second eigenvalue problem can be transformed to that of the transfer matrix of the inhomogeneous XXX spin chain, which allows us to obtain the spectrum of the Hamiltonian and the associated Bethe ansatz equations by the off-diagonal Bethe ansatz method.

math-ph↗
arXiv2013

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.

cond-mat.str-el↗
arXiv2013

Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields

The anisotropic spin-1/2 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 ansatzs and the corresponding Bethe ansatz equations are derived.

cond-mat.stat-mech↗
arXiv2013

Off-diagonal Bethe ansatz and exact solution of a topological spin ring

A general method is proposed for constructing the Bethe ansatz equations of integrable models without U(1) symmetry. As an example, the exact spectrum of the XXZ spin ring with M{\" o}bius like topological boundary condition is derived by constructing a modified T-Q relation based on the functional connection between the eigenvalues of the transfer matrix and the quantum determinant of the monodromy matrix. With the exact solution, the elementary excitations of the topological XX spin ring is discussed in detail. It is found that the excitation spectrum indeed shows a nontrivial topological nature.

cond-mat.stat-mech↗
arXiv1999

The Thermodynamics of the XXZ Heisenberg Chain with Impurities

In this paper, we discuss the effect of the arbitrary spin impurities to the spin-1/2 and spin-1 XXZ model. The effect of ground state, the free energy, the magnetic susceptibility, the specific heat and the Kondo temperature are given by using the thermodynamic Bethe ansatz equation.

cond-mat↗