7,922 research outputs found
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
Fermionic screening operators in the sine-Gordon model
Extending our previous construction in the sine-Gordon model, we show how to
introduce two kinds of fermionic screening operators, in close analogy with
conformal field theory with c<1.Comment: 18 pages, 1 figur
Minimal Gauge Invariant Classes of Tree Diagrams in Gauge Theories
We describe the explicit construction of groves, the smallest gauge invariant
classes of tree Feynman diagrams in gauge theories. The construction is valid
for gauge theories with any number of group factors which may be mixed. It
requires no summation over a complete gauge group multiplet of external matter
fields. The method is therefore suitable for defining gauge invariant classes
of Feynman diagrams for processes with many observed final state particles in
the standard model and its extensions.Comment: 13 pages, RevTeX (EPS figures
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 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
Connecting lattice and relativistic models via conformal field theory
We consider the quantum group invariant XXZ-model. In infrared limit it
describes Conformal Field Theory with modified energy-momentum tensor. The
correlation functions are related to solutions of level -4 of qKZ equations. We
describe these solutions relating them to level 0 solutions. We further
consider general matrix elements (form factors) containing local operators and
asymptotic states. We explain that the formulae for solutions of qKZ equations
suggest a decomposition of these matrix elements with respect to states of
corresponding Conformal Field Theory .Comment: 22 pages, 1 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
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
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