On the algebraic Bethe ansatz approach to the correlation functions of the XXZ spin-1/2 Heisenberg chain (original) (raw)

Correlation functions of the XXZ Heisenberg spin chain: Bethe ansatz approach

We review recent progress in the computation of correlation functions of the XXZ spin-1/2 chain. We describe both finite and infinite chain results. Long distance asymptotic behavior is discussed. Our method is based on the resolution of the quantum inverse scattering problem in the framework of the algebraic Bethe ansatz.

Correlation Functions of the XXZ Spin-½ Heisenberg Chain: Recent Advances (Review)

International Journal of Modern Physics A, 2004

We review some recent advances in the computation of exact correlation functions of the XXZ-½ Heisenberg chain. We first give a general introduction to our method which is based on the algebraic Bethe ansatz and the resolution of the quantum inverse scattering problem, leading in particular to multiple integral representations for the correlation functions. Then we describe recently obtained compact formulas for the spin-spin correlation functions of the XXZ-½ Heisenberg chain. We outline how this leads to several explicit results including the known two point functions in the limit of free fermions, the so-called emptiness formation probability at anisotropy Δ=1/2 and its large distance asymptotic behaviour in the massless phase of the model.

Correlation functions of the XXZ Heisenberg spin- chain in a magnetic field

Nuclear Physics B, 2000

Using the algebraic Bethe ansatz method, and the solution of the quantum inverse scattering problem for local spins, we obtain multiple integral representations of the n-point correlation functions of the XXZ Heisenberg spin-1 2 chain in a constant magnetic field. For zero magnetic field, this result agrees, in both the massless and massive (anti-ferromagnetic) regimes, with the one obtained from the q-deformed KZ equations (massless regime) and the representation theory of the quantum affine algebra U q (ŝl 2) together with the corner transfer matrix approach (massive regime).

Spin–spin correlation functions of the XXZ- Heisenberg chain in a magnetic field

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.

Algebraic Representation of Correlation Functions in Integrable Spin Chains

Annales Henri Poincaré, 2006

Taking the XXZ chain as the main example, we give a review of an algebraic representation of correlation functions in integrable spin chains obtained recently. We rewrite the previous formulas in a form which works equally well for the physically interesting homogeneous chains. We discuss also the case of quantum group invariant operators and generalization to the XYZ chain.

Third-neighbor and other four-point correlation functions of spin-1/2 XXZ chain

2004

The correlation functions of the spin-1/2 XXZ chain in the ground state were expressed in the form of multiple integrals for -1<\Delta \leq 1 and 1<\Delta. In particular, adjacent four-point correlation functions were given as certain four-dimensional integrals. We show that these integrals can be reduced to polynomials with respect to specific one-dimensional integrals. The results give the polynomial representation of the third-neighbor correlation functions.