Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA new integral representation for the scalar products of Bethe states for the XXX spin chain
156
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Based on the method of separation of variables due to Sklyanin, we construct a new integral representation for the scalar products of the Bethe states for the SU(2) XXX spin 1/2 chain obeying the periodic boundary condition. Due to the compactness of the symmetry group, a twist matrix must be introduced at the boundary in order to extract the separated variables properly. Then by deriving the integration measure and the spectrum of the separated variables, we express the inner product of an on-shell and an off-shell Bethe states in terms of a multiple contour integral involving a product of Baxter wave functions. Its form is reminiscent of the integral over the eigenvalues of a matrix model and is expected to be useful in studying the semi-classical limit of the product.
rate research
Read More
We study the inner product of Bethe states in the inhomogeneous periodic XXX spin-1/2 chain of length L, which is given by the Slavnov determinant formula. We show that the inner product of an on-shell M-magnon state with a generic M-magnon state is given by the same expression as the inner product of a 2M-magnon state with a vacuum descendent. The second inner product is proportional to the partition function of the six-vertex model on a rectangular Lx2M grid, with partial domain-wall boundary conditions.
We consider the integrable open-chain transfer matrix corresponding to a Y=0 brane at one boundary, and a Y_theta=0 brane (rotated with the respect to the former by an angle theta) at the other boundary. We determine the exact eigenvalues of this transfer matrix in terms of solutions of a corresponding set of Bethe equations.
In our previous works on the XXZ chain of spin one half, we have studied the problem of constructing a basis of local operators whose members have simple vacuum expectation values. For this purpose a pair of fermionic creation operators have been introduced. In this article we extend this construction to the spin one case. We formulate the fusion procedure for the creation operators, and find a triplet of bosonic as well as two pairs of fermionic creation operators. We show that the resulting basis of local operators satisfies the dual reduced qKZ equation.
The periodic $OSp(1|2)$ quantum spin chain has both a graded and a non-graded version. Naively, the Bethe ansatz solution for the non-graded version does not account for the complete spectrum of the transfer matrix, and we propose a simple mechanism for achieving completeness. In contrast, for the graded version, this issue does not arise. We also clarify the symmetries of bot
We consider closed XXX spin chains with broken total spin $U(1)$ symmetry within the framework of the modified algebraic Bethe ansatz. We study multiple actions of the modified monodromy matrix entries on the modified Bethe vectors. The obtained formulas of the multiple actions allow us to calculate the scalar products of the modified Bethe vectors. We find an analog of Izergin-Korepin formula for the scalar products. This formula involves modified Izergin determinants and can be expressed as sums over partitions of the Bethe parameters.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
