27 research outputs found
Algebraic representation of correlation functions in integrable spin chains
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.Comment: 31 pages, no figur
A recursion formula for the correlation functions of an inhomogeneous XXX model
A new recursion formula is presented for the correlation functions of the
integrable spin 1/2 XXX chain with inhomogeneity. It relates the correlators
involving n consecutive lattice sites to those with n-1 and n-2 sites. In a
series of papers by V. Korepin and two of the present authors, it was
discovered that the correlators have a certain specific structure as functions
of the inhomogeneity parameters. Our formula allows for a direct proof of this
structure, as well as an exact description of the rational functions which has
been left undetermined in the previous works.Comment: 37 pages, 1 figure, Proof of Lemma 4.8 modifie
Fifth-neighbor spin-spin correlator for the anti-ferromagnetic Heisenberg chain
We study the generating function of the spin-spin correlation functions in
the ground state of the anti-ferromagnetic spin-1/2 Heisenberg chain without
magnetic field. We have found its fundamental functional relations from those
for general correlation functions, which originate in the quantum
Knizhink-Zamolodchikov equation. Using these relations, we have calculated the
explicit form of the generating functions up to n=6. Accordingly we could
obtain the spin-spin correlator up to k=5.Comment: 10 page
Finite temperature density matrix and two-point correlations in the antiferromagnetic XXZ chain
We derive finite temperature versions of integral formulae for the two-point
correlation functions in the antiferromagnetic XXZ chain. The derivation is
based on the summation of density matrix elements characterizing a finite chain
segment of length . On this occasion we also supply a proof of the basic
integral formula for the density matrix presented in an earlier publication.Comment: 35 page
Exact evaluation of density matrix elements for the Heisenberg chain
We have obtained all the density matrix elements on six lattice sites for the
spin-1/2 Heisenberg chain via the algebraic method based on the quantum
Knizhnik-Zamolodchikov equations. Several interesting correlation functions,
such as chiral correlation functions, dimer-dimer correlation functions, etc...
have been analytically evaluated. Furthermore we have calculated all the
eigenvalues of the density matrix and analyze the eigenvalue-distribution. As a
result the exact von Neumann entropy for the reduced density matrix on six
lattice sites has been obtained.Comment: 33 pages, 4 eps figures, 3 author
Short-distance thermal correlations in the XXZ chain
Recent studies have revealed much of the mathematical structure of the static
correlation functions of the XXZ chain. Here we use the results of those
studies in order to work out explicit examples of short-distance correlation
functions in the infinite chain. We compute two-point functions ranging over 2,
3 and 4 lattice sites as functions of the temperature and the magnetic field
for various anisotropies in the massless regime . It turns
out that the new formulae are numerically efficient and allow us to obtain the
correlations functions over the full parameter range with arbitrary precision.Comment: 25 pages, 5 colored figure
Exact results for the sigma^z two-point function of the XXZ chain at Delta=1/2
We propose a new multiple integral representation for the correlation
function of the XXZ spin-1/2 Heisenberg chain in the
disordered regime. We show that for Delta=1/2 the integrals can be separated
and computed exactly. As an example we give the explicit results up to the
lattice distance m=8. It turns out that the answer is given as integer numbers
divided by 2^[(m+1)^2].Comment: 8 page
Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
We present a conjecture for the density matrix of a finite segment of the XXZ
chain coupled to a heat bath and to a constant longitudinal magnetic field. It
states that the inhomogeneous density matrix, conceived as a map which
associates with every local operator its thermal expectation value, can be
written as the trace of the exponential of an operator constructed from
weighted traces of the elements of certain monodromy matrices related to and only two transcendental functions pertaining to
the one-point function and the neighbour correlators, respectively. Our
conjecture implies that all static correlation functions of the XXZ chain are
polynomials in these two functions and their derivatives with coefficients of
purely algebraic origin.Comment: 35 page
Traces on the Sklyanin algebra and correlation functions of the eight-vertex model
We propose a conjectural formula for correlation functions of the Z-invariant
(inhomogeneous) eight-vertex model. We refer to this conjecture as Ansatz. It
states that correlation functions are linear combinations of products of three
transcendental functions, with theta functions and derivatives as coefficients.
The transcendental functions are essentially logarithmic derivatives of the
partition function per site. The coefficients are given in terms of a linear
functional on the Sklyanin algebra, which interpolates the usual trace on
finite dimensional representations. We establish the existence of the
functional and discuss the connection to the geometry of the classical limit.
We also conjecture that the Ansatz satisfies the reduced qKZ equation. As a
non-trivial example of the Ansatz, we present a new formula for the
next-nearest neighbor correlation functions.Comment: 35 pages, 2 figures, final versio
Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
We compute all dynamical spin-spin correlation functions for the spin-1/2
anisotropic Heisenberg model in the gapless antiferromagnetic regime,
using numerical sums of exact determinant representations for form factors of
spin operators on the lattice. Contributions from intermediate states
containing many particles and string (bound) states are included. We present
modified determinant representations for the form factors valid in the general
case with string solutions to the Bethe equations. Our results are such that
the available sum rules are saturated to high precision. We Fourier transform
our results back to real space, allowing us in particular to make a comparison
with known exact formulas for equal-time correlation functions for small
separations in zero field, and with predictions for the zero-field asymptotics
from conformal field theory.Comment: 14 page