16 research outputs found
Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
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.Comment: 34 page
Correlation functions of the XXZ spin-1/2 Heisenberg chain at the free fermion point from their multiple integral representations
Using multiple integral representations, we derive exact expressions for the
correlation functions of the spin-1/2 Heisenberg chain at the free fermion
point.Comment: 24 pages, LaTe
Dynamical correlation functions of the XXZ spin-1/2 chain
We derive a master equation for the dynamical spin-spin correlation functions
of the XXZ spin-1/2 Heisenberg finite chain in an external magnetic field. In
the thermodynamic limit, we obtain their multiple integral representation.Comment: 25 page
Master equation for spin-spin correlation functions of the XXZ chain
We derive a new representation for spin-spin correlation functions of the
finite XXZ spin-1/2 Heisenberg chain in terms of a single multiple integral,
that we call the master equation. Evaluation of this master equation gives rise
on the one hand to the previously obtained multiple integral formulas for the
spin-spin correlation functions and on the other hand to their expansion in
terms of the form factors of the local spin operators. Hence, it provides a
direct analytic link between these two representations of the correlation
functions and a complete re-summation of the corresponding series. The master
equation method also allows one to obtain multiple integral representations for
dynamical correlation functions.Comment: 24 page
Correlation functions for a strongly correlated boson system
The correlation functions for a strongly correlated exactly solvable
one-dimensional boson system on a finite chain as well as in the thermodynamic
limit are calculated explicitly. This system which we call the phase model is
the strong coupling limit of the integrable q-boson hopping model. The results
are presented as determinants.Comment: 27 pages LaTe
Superconducting correlations in metallic nanoparticles: exact solution of the BCS model by the algebraic Bethe ansatz
Superconducting pairing of electrons in nanoscale metallic particles with
discrete energy levels and a fixed number of electrons is described by the
reduced BCS model Hamiltonian. We show that this model is integrable by the
algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators,
integrals of motion, and norms of wave functions are obtained. Furthermore, the
quantum inverse problem is solved, meaning that form factors and correlation
functions can be explicitly evaluated. Closed form expressions are given for
the form factors that describe superconducting pairing.Comment: revised version, 5 pages, revtex, no figure
Yang-Mills Correlation Functions from Integrable Spin Chains
The relation between the dilatation operator of N=4 Yang-Mills theory and
integrable spin chains makes it possible to compute the one-loop anomalous
dimensions of all operators in the theory. In this paper we show how to apply
the technology of integrable spin chains to the calculation of Yang-Mills
correlation functions by expressing them in terms of matrix elements of spin
operators on the corresponding spin chain. We illustrate this method with
several examples in the SU(2) sector described by the XXX_1/2 chain.Comment: 27 pages, 3 figures, harvma
On the algebraic Bethe Ansatz approach to the correlation functions of the XXZ spin-1/2 Heisenberg chain
35 pages, review articleWe 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