284 research outputs found
Factorizing -matrices and the XXZ spin-1/2 chain: A diagrammatic perspective
Using notation inherited from the six-vertex model, we construct diagrams
that represent the action of the factorizing -matrices associated to the
finite length XXZ spin-1/2 chain. We prove that these -matrices factorize
the tensor corresponding with elements of the permutation
group. We consider in particular the diagram for the tensor , which cyclically permutes the spin chain. This leads us to a diagrammatic
construction of the local spin operators and in terms of
the monodromy matrix operators.Comment: 26 pages, extra references added, typographical errors correcte
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
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
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
Emptiness formation probability at finite temperature for the isotropic Heisenberg chain
We present an integral formula for a special correlation function of the
isotropic spin-1/2 antiferromagnetic Heisenberg chain. The correlation function
describes the probability for the occurrence of a string of consecutive
up-spins as a function of temperature, magnetic field and length of the string.Comment: 3 pages, 1 figure, submitted to SCES'0
Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End
In this paper we consider two a priori very different problems: construction
of the eigenstates of the spin chains with non parallel boundary magnetic
fields and computation of the partition function for the trigonometric
solid-on-solid (SOS) model with one reflecting end and domain wall boundary
conditions. We show that these two problems are related through a gauge
transformation (so-called vertex-face transformation) and can be solved using
the same dynamical reflection algebras.Comment: based on a talk given at RAQIS'10, Recent Advances in Quantum
Integrable Systems, Annecy-le-Vieux, France, 15-18 June 201
Coordinate space wave function from the Algebraic Bethe Ansatz for the inhomogeneous six-vertex model
We derive the coordinate space wave function for the inhomogeneous six-vertex
model from the Algebraic Bethe Ansatz. The result is in agreement with the
result first obtained long time ago by Yang and Gaudin in the context of the
problem of one-dimensional fermions with delta- function interaction.Comment: 7 pages, LaTe
Partition function of the trigonometric SOS model with reflecting end
We compute the partition function of the trigonometric SOS model with one
reflecting end and domain wall type boundary conditions. We show that in this
case, instead of a sum of determinants obtained by Rosengren for the SOS model
on a square lattice without reflection, the partition function can be
represented as a single Izergin determinant. This result is crucial for the
study of the Bethe vectors of the spin chains with non-diagonal boundary terms.Comment: 13 pages, improved versio
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
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