35 research outputs found
Semi-classical scalar products in the generalised SU(2) model
In these notes we review the field-theoretical approach to the computation of
the scalar product of multi-magnon states in the Sutherland limit where the
magnon rapidities condense into one or several macroscopic arrays. We formulate
a systematic procedure for computing the 1/M expansion of the
on-shell/off-shell scalar product of M-magnon states in the generalised
integrable model with SU(2)-invariant rational R-matrix. The coefficients of
the expansion are obtained as multiple contour integrals in the rapidity plane.Comment: 13 pages, 3 figures. Based on a talk delivered at the X.
International Workshop "Lie Theory and Its Applications in Physics", (LT-10),
Varna, Bulgaria, 17-23 June 201
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
Multiple Actions of the Monodromy Matrix in gl(2|1)-Invariant Integrable Models
We study gl(2|1) symmetric integrable models solvable by the nested algebraic Bethe ansatz. Using explicit formulas for the Bethe vectors we derive the actions of the monodromy matrix entries onto these vectors. We show that the result of these actions is a finite linear combination of Bethe vectors. The obtained formulas open a way for studying scalar products of Bethe vectors
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
Scalar products in generalized models with SU(3)-symmetry
We consider a generalized model with SU(3)-invariant R-matrix, and review the
nested Bethe Ansatz for constructing eigenvectors of the transfer matrix. A sum
formula for the scalar product between generic Bethe vectors, originally
obtained by Reshetikhin [11], is discussed. This formula depends on a certain
partition function Z(\{\lambda\},\{\mu\}|\{w\},\{v\}), which we evaluate
explicitly. In the limit when the variables \{\mu\} or \{v\} approach infinity,
this object reduces to the domain wall partition function of the six-vertex
model Z(\{\lambda\}|\{w\}). Using this fact, we obtain a new expression for the
off-shell scalar product (between a generic Bethe vector and a Bethe
eigenvector), in the case when one set of Bethe variables tends to infinity.
The expression obtained is a product of determinants, one of which is the
Slavnov determinant from SU(2) theory. It extends a result of Caetano [13].Comment: 28 pages, 12 figures, greatly lengthened exposition in v3; 2
appendices and extra references adde
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 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
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