55 research outputs found
Asymptotic form of two-point correlation function of the XXZ spin chain
Correlation functions of the XXZ spin chain in the critical regime is studied
at zero-temperature. They are exactly represented in the Fredholm determinant
form and are related with an operator-valued Riemann-Hilbert problem. Analyzing
this problem we prove that a two-point correlation function consisting of
sufficiently separated spin operators is expressed by power-functions of the
distance between those operators.Comment: 9 pages, LaTeX2e (+ amssymb, amsthm); Proof of Lemma 1 is revise
The Hubbard chain: Lieb-Wu equations and norm of the eigenfunctions
We argue that the square of the norm of the Hubbard wave function is
proportional to the determinant of a matrix, which is obtained by linearization
of the Lieb-Wu equations around a solution. This means that in the vicinity of
a solution the Lieb-Wu equations are non-degenerate, if the corresponding wave
function is non-zero. We further derive an action that generates the Lieb-Wu
equations and express our determinant formula for the square of the norm in
terms of the Hessian determinant of this action.Comment: 11 pages, Late
A note on density correlations in the half-filled Hubbard model
We consider density-density correlations in the one-dimensional Hubbard model
at half filling. On intuitive grounds one might expect them to exhibit an
exponential decay. However, as has been noted recently, this is not obvious
from the Bethe Ansatz/conformal field theory (BA/CFT) approach. We show that by
supplementing the BA/CFT analysis with simple symmetry arguments one can easily
prove that correlations of the lattice density operators decay exponentially.Comment: 3 pages, RevTe
Spectrum of boundary states in the open Hubbard chain
We use the Bethe Ansatz solution for the one dimensional Hubbard model with
open boundary conditions and applied boundary fields to study the spectrum of
bound states at the boundary. Depending on the strength of the boundary
potentials one finds that the true ground state contains a single charge or,
for boundary potentials comparable to the Hubbard interaction, a pair of
electrons in a bound state. If these are left unoccupied one finds holon and
spinon bound states. We compute the finite size corrections to the low lying
energies in this system and use the predictions of boundary conformal field
theory to study the exponents related to the orthogonality catastrophe.Comment: LaTeX + epsf,amssymb macros, 14 pp. incl. figure
Form factors of boundary fields for A(2)-affine Toda field theory
In this paper we carry out the boundary form factor program for the
A(2)-affine Toda field theory at the self-dual point. The latter is an
integrable model consisting of a pair of particles which are conjugated to each
other and possessing two bound states resulting from the scattering processes 1
+1 -> 2 and 2+2-> 1. We obtain solutions up to four particle form factors for
two families of fields which can be identified with spinless and spin-1 fields
of the bulk theory. Previously known as well as new bulk form factor solutions
are obtained as a particular limit of ours. Minimal solutions of the boundary
form factor equations for all A(n)-affine Toda field theories are given, which
will serve as starting point for a generalisation of our results to higher rank
algebras.Comment: 24 pages LaTeX, 1 figur
Consistent Batalin--Fradkin quantization of Infinitely Reducible First Class Constraints
We reconsider the problem of BRST quantization of a mechanics with infinitely
reducible first class constraints. Following an earlier recipe [Phys. Lett. B
381, 105, (1996)], the original phase space is extended by purely auxiliary
variables, the constraint set in the enlarged space being first stage of
reducibility. The BRST charge involving only a finite number of ghost variables
is explicitly constructed.Comment: 5 pages, LaTex. Minor corrections including the title. The version to
appear in Phys. Rev.
Spontaneous Breaking of Translational Invariance in One-Dimensional Stationary States on a Ring
We consider a model in which positive and negative particles diffuse in an
asymmetric, CP-invariant way on a ring. The positive particles hop clockwise,
the negative counterclockwise and oppositely-charged adjacent particles may
swap positions. Monte-Carlo simulations and analytic calculations suggest that
the model has three phases; a "pure" phase in which one has three pinned blocks
of only positive, negative particles and vacancies, and in which translational
invariance is spontaneously broken, a "mixed" phase with a non-vanishing
current in which the three blocks are positive, negative and neutral, and a
disordered phase without blocks.Comment: 7 pages, LaTeX, needs epsf.st
model as effective Hamiltonian for generalized Hubbard models with broken -symmetry
We consider the limit of strong Coulomb attraction for generalized Hubbard
models with -symmetry. In this limit these models are equivalent to the
ferromagnetic spin-1/2 Heisenberg quantum spin chain. In order to study the
behaviour of the superconducting phase in the electronic model under
perturbations which break the -symmetry we investigate the ground state
of the ferromagnetic non-critical -chain in the sector with fixed
magnetization. It turns out to be a large bound state of magnons. We find
that the perturbations considered here lead to the disappearance of the
off-diagonal longe-range order.Comment: Results of previous version are generalized, new title, references
added. 10 pages, Latex, no figure
Boundary form factors of the sinh-Gordon model with Dirichlet boundary conditions at the self-dual point
In this manuscript we present a detailed investigation of the form factors of
boundary fields of the sinh-Gordon model with a particular type of Dirichlet
boundary condition, corresponding to zero value of the sinh-Gordon field at the
boundary, at the self-dual point. We follow for this the boundary form factor
program recently proposed by Z. Bajnok, L. Palla and G. Takaks in
hep-th/0603171, extending the analysis of the boundary sinh-Gordon model
initiated there. The main result of the paper is a conjecture for the structure
of all n-particle form factors of two particular boundary operators in terms of
elementary symmetric polynomials in certain functions of the rapidity
variables. In addition, form factors of boundary "descendant" fields have been
constructedComment: 14 pages LaTex. Version to appear in J. Phys.
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