10,372 research outputs found
High energy QCD as a completely integrable model
We show that the one-dimensional lattice model proposed by Lipatov to
describe the high energy scattering of hadrons in multicolor QCD is completely
integrable. We identify this model as the XXX Heisenberg chain of noncompact
spin and find the conservation laws of the model. A generalized Bethe
ansatz is developed for the diagonalization of the hamiltonian and for the
calculation of hadron-hadron scattering amplitude.Comment: Latex style, 16 pages, ITP-SB-94-1
Complete Pseudohole and Heavy-Pseudoparticle Operator Representation for the Hubbard Chain
We introduce the pseudohole and heavy-pseudoparticle operator algebra that
generates all Hubbard-chain eigenstates from a single reference vacuum. In
addition to the pseudoholes already introduced for the description of the
low-energy physics, this involves the heavy pseudoparticles associated with
Hamiltonian eigenstates whose energy spectrum has a gap relatively to the
many-electron ground state. We introduce a generalized pseudoparticle
perturbation theory which describes the relevant finite-energy ground state
transitions. In the present basis these excitations refer to a small density of
excited pseudoparticles. Our operator basis goes beyond the Bethe-ansatz
solution and it is the suitable and correct starting point for the study of the
finite-frequency properties, which are of great relevance for the understanding
of the unusual spectral properties detected in low-dimensional novel materials.Comment: LaTeX, 32 pages, no Figures. To be published in Phys. Rev. B (15th of
August 1997
Introduction to Quantum Integrability
In this article we review the basic concepts regarding quantum integrability.
Special emphasis is given on the algebraic content of integrable models. The
associated algebras are essentially described by the Yang-Baxter and boundary
Yang-Baxter equations depending on the choice of boundary conditions. The
relation between the aforementioned equations and the braid group is briefly
discussed. A short review on quantum groups as well as the quantum inverse
scattering method (algebraic Bethe ansatz) is also presented.Comment: 56 pages, Latex. A few typos correcte
Construction and exact solution of a nonlinear quantum field model in quasi-higher dimension
Nonperturbative exact solutions are allowed for quantum integrable models in
one space-dimension. Going beyond this class we propose an alternative Lax
matrix approach, exploiting the hidden multi-time concept in integrable systems
and construct a novel quantum nonlinear Schroedinger model in quasi-two
dimensions. An intriguing field commutator is discovered, confirming the
integrability of the model and yielding its exact Bethe ansatz solution with
rich scattering and bound-state properties. The universality of the scheme is
expected to cover diverse models, opening up a new direction in the field.Comment: 12 pages, 1 figure, Latex (This version to be published in Nucl Phys
B as Frontiers Article
On correlation functions of integrable models associated to the six-vertex R-matrix
We derive an analog of the master equation obtained recently for correlation
functions of the XXZ chain for a wide class of quantum integrable systems
described by the R-matrix of the six-vertex model, including in particular
continuum models. This generalized master equation allows us to obtain multiple
integral representations for the correlation functions of these models. We
apply this method to derive the density-density correlation functions of the
quantum non-linear Schrodinger model.Comment: 21 page
Integrable approach to simple exclusion processes with boundaries. Review and progress
We study the matrix ansatz in the quantum group framework, applying
integrable systems techniques to statistical physics models. We start by
reviewing the two approaches, and then show how one can use the former to get
new insight on the latter. We illustrate our method by solving a model of
reaction-diffusion. An eigenvector for the transfer matrix for the XXZ spin
chain with non-diagonal boundary is also obtained using a matrix ansatz.Comment: 44 page
On determinant representations of scalar products and form factors in the SoV approach: the XXX case
In the present article we study the form factors of quantum integrable
lattice models solvable by the separation of variables (SoV) method. It was
recently shown that these models admit universal determinant representations
for the scalar products of the so-called separate states (a class which
includes in particular all the eigenstates of the transfer matrix). These
results permit to obtain simple expressions for the matrix elements of local
operators (form factors). However, these representations have been obtained up
to now only for the completely inhomogeneous versions of the lattice models
considered. In this article we give a simple algebraic procedure to rewrite the
scalar products (and hence the form factors) for the SoV related models as
Izergin or Slavnov type determinants. This new form leads to simple expressions
for the form factors in the homogeneous and thermodynamic limits. To make the
presentation of our method clear, we have chosen to explain it first for the
simple case of the Heisenberg chain with anti-periodic boundary
conditions. We would nevertheless like to stress that the approach presented in
this article applies as well to a wide range of models solved in the SoV
framework.Comment: 46 page
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