Master equation for spin–spin correlation functions of the chain (original) (raw)
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Nuclear Physics B, 2002
Using algebraic Bethe ansatz and the solution of the quantum inverse scattering problem, we compute compact representations of the spin-spin correlation functions of the XXZ-1 2 Heisenberg chain in a magnetic field. At lattice distance m, they are typically given as the sum of m terms. Each term n of this sum, n = 1,. .. m, is represented in the thermodynamic limit as a multiple integral of order 2n + 1; the integrand depends on the distance as the power m of some simple function. The root of these results is the derivation of a compact formula for the multiple action on a general quantum state of the chain of transfer matrix operators for arbitrary values of their spectral parameters.
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SciPost Physics, 2021
We explain how to compute correlation functions at zero temperature within the framework of the quantum version of the Separation of Variables (SoV) in the case of a simple model: the XXX Heisenberg chain of spin 1/2 with twisted (quasi-periodic) boundary conditions. We first detail all steps of our method in the case of anti-periodic boundary conditions. The model can be solved in the SoV framework by introducing inhomogeneity parameters. The action of local operators on the eigenstates are then naturally expressed in terms of multiple sums over these inhomogeneity parameters. We explain how to transform these sums over inhomogeneity parameters into multiple contour integrals. Evaluating these multiple integrals by the residues of the poles outside the integration contours, we rewrite this action as a sum involving the roots of the Baxter polynomial plus a contribution of the poles at infinity. We show that the contribution of the poles at infinity vanishes in the thermodynamic lim...
Quantum Integrals of Motion for the Heisenberg Spin Chain
Modern Physics Letters A, 1994
An explicit expression for all the quantum integrals of motion for the isotropic Heisenberg s=1/2 spin chain is presented. The conserved quantities are expressed in terms of a sum over simple polynomials in spin variables. This construction is direct and independent of the transfer matrix formalism. Continuum limits of these integrals in both ferromagnetic and antiferromagnetic sectors are briefly discussed.
We present a review of the method we have elaborated to compute the correlation functions of the XXZ spin-1/2 Heisenberg chain. This method is based on the resolution of the quantum inverse scattering problem in the algebraic Bethe Ansatz framework, and leads to a multiple integral representation of the dynamical correlation functions. We describe in particular some recent advances concerning the two-point functions: in the finite chain, they can be expressed in terms of a single multiple integral. Such a formula provides a direct analytic connection between the previously obtained multiple integral representations and the form factor expansions for the correlation functions.