scholarly journals From Quantum Affine Groups to the Exact Dynamical Correlation Function of the Heisenberg Model

1997 ◽  
Vol 11 (01n02) ◽  
pp. 103-107
Author(s):  
A. H. Bougourzi ◽  
M. Couture ◽  
M. Kacir
Keyword(s):  
Correlation Function ◽  
Form Factors ◽  
Exact Formula ◽  
Exact Form ◽  
Zero Temperature ◽  
Dynamical Correlation ◽  
Xxz Model ◽  
Affine Groups ◽  
Affine Symmetry ◽  
Xxx Model

The exact form factors of the Heisenberg models XXX and XXZ have been recently computed through the quantum affine symmetry of XXZ model in the thermodynamic limit. We use them to derive an exact formula for the contribution of two spinons to the dynamical correlation function of XXX model at zero temperature.

SOME INTEGRAL FORMULAS FOR THE SOLUTIONS OF THE sl2 dKZ EQUATION WITH LEVEL −4

1994 ◽  
Vol 09 (32) ◽  
pp. 5673-5687 ◽  
Author(s):  
ATSUSHI NAKAYASHIKI
Keyword(s):  
Correlation Function ◽  
Integral Formula ◽  
Time Integration ◽  
Direct Proof ◽  
Vertex Operators ◽  
Type I ◽  
Xxz Model ◽  
Integral Formulas ◽  
Xxx Model

A direct proof is given for the fact that the integral formula for the XXX limit of the trace of the type I q-vertex operators satisfies the deformed Knizhnik-Zamolodchikov (dKZ) equation with level −4. We have also carried out one-time integration by taking the residue at infinity. As a corollary of these we can construct a family of the integral formulas for solutions to the dKZ equation. Another corollary is the integral formula for the correlation function of the inhomogeneous XXX model, whose number of integrals is less than that of the previously obtained correlator for the XXZ model.

scholarly journals Approaching the self-dual point of the sinh-Gordon model

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Robert Konik ◽  
Márton Lájer ◽  
Giuseppe Mussardo
Keyword(s):  
Small Volume ◽  
Zero Mode ◽  
Form Factors ◽  
Lagrangian Formulation ◽  
The Self ◽  
Quantum Mechanical ◽  
Exact Form ◽  
Coupling Constant ◽  
Self Duality ◽  
Hyperbolic Cosine

Abstract One of the most striking but mysterious properties of the sinh-Gordon model (ShG) is the b → 1/b self-duality of its S-matrix, of which there is no trace in its Lagrangian formulation. Here b is the coupling appearing in the model’s eponymous hyperbolic cosine present in its Lagrangian, cosh(bϕ). In this paper we develop truncated spectrum methods (TSMs) for studying the sinh-Gordon model at a finite volume as we vary the coupling constant. We obtain the expected results for b ≪ 1 and intermediate values of b, but as the self-dual point b = 1 is approached, the basic application of the TSM to the ShG breaks down. We find that the TSM gives results with a strong cutoff Ec dependence, which disappears according only to a very slow power law in Ec. Standard renormalization group strategies — whether they be numerical or analytic — also fail to improve upon matters here. We thus explore three strategies to address the basic limitations of the TSM in the vicinity of b = 1. In the first, we focus on the small-volume spectrum. We attempt to understand how much of the physics of the ShG is encoded in the zero mode part of its Hamiltonian, in essence how ‘quantum mechanical’ vs ‘quantum field theoretic’ the problem is. In the second, we identify the divergencies present in perturbation theory and perform their resummation using a supra-Borel approximate. In the third approach, we use the exact form factors of the model to treat the ShG at one value of b as a perturbation of a ShG at a different coupling. In the light of this work, we argue that the strong coupling phase b > 1 of the Lagrangian formulation of model may be different from what is naïvely inferred from its S-matrix. In particular, we present an argument that the theory is massless for b > 1.

QUANTUM MAGNETIC VORTICES AT FINITE TEMPERATURE IN (3 + 1)-D

2000 ◽  
Vol 15 (11n12) ◽  
pp. 731-735
Author(s):  
E. C. MARINO ◽  
D. G. G. SASAKI
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Large Distance ◽  
Finite Temperature ◽  
Higgs Model ◽  
Magnetic Vortex ◽  
Zero Temperature ◽  
Magnetic Vortices ◽  
Vortex Lines ◽  
Distance Behavior

We study the effect of a finite temperature on the correlation function of quantum magnetic vortex lines in the framework of the (3 + 1)-dimensional Abelian Higgs model. The vortex energy is inferred from the large distance behavior of these correlation functions. For large straight vortices of length L, we obtain that the energy is proportional to TL2 differently from the zero temperature result which is proportional to L. The case of closed strings is also analyzed. For T = 0, we evaluate the correlation function and energy of a large ring. Finite closed vortices do not exist as genuine excitations for any temperature.

scholarly journals Exact two-spinon dynamical correlation function of the one-dimensional Heisenberg model

1996 ◽  
Vol 54 (18) ◽  
pp. R12669-R12672 ◽  
Author(s):  
A. H. Bougourzi ◽  
M. Couture ◽  
M. Kacir
Keyword(s):  
Correlation Function ◽  
Heisenberg Model ◽  
Dynamical Correlation ◽  
One Dimensional ◽  
The One

scholarly journals The nestedSU(N) off-shell Bethe ansatz and exact form factors

2008 ◽  
Vol 41 (27) ◽  
pp. 275202 ◽  
Author(s):  
H Babujian ◽  
A Foerster ◽  
M Karowski
Keyword(s):  
Bethe Ansatz ◽  
Form Factors ◽  
Exact Form

CORRELATION FUNCTIONS OF INTEGRABLE 2D MODELS OF THE RELATIVISTIC FIELD THEORY: ISING MODEL

1991 ◽  
Vol 06 (19) ◽  
pp. 3419-3440 ◽  
Author(s):  
V.P. YUROV ◽  
AL. B. ZAMOLODCHIKOV
Keyword(s):  
Magnetic Field ◽  
Correlation Functions ◽  
Form Factors ◽  
Field Theories ◽  
Scattering Data ◽  
Exact Form ◽  
Relativistic Field ◽  
Spin Correlations ◽  
Ising Spin ◽  
Infinite Sums

A program is proposed to study numerically the correlation functions in massive integrable 2D relativistic field theories. It relies crucially on the exact form factors of fields which can be reconstructed from the factorized scattering data. The correlation functions are expressible as infinite sums over intermediate asymptotic states. We suggest using computer power to perform the summation numerically. The convergence of the sum is tested for the simplest example of the scaling Ising spin-spin correlations (without magnetic field).

Method of separated form factors for polydisperse vesicles

2006 ◽  
Vol 39 (3) ◽  
pp. 293-303 ◽  
Author(s):  
Jeremy Pencer ◽  
Susan Krueger ◽  
Carl P. Adams ◽  
John Katsaras
Keyword(s):  
Form Factor ◽  
Laplace Transform ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Scattering Length ◽  
Form Factors ◽  
Particle Sizes ◽  
Exact Form ◽  
The Laplace Transform ◽  
Spherical Vesicles

Use of the Schulz or Gamma distribution in the description of particle sizes facilitates calculation of analytic polydisperse form factors using Laplace transforms, {\cal L}[f(u)]. Here, the Laplace transform approach is combined with the separated form factor (SFF) approximation [Kiselevet al.(2002).Appl. Phys. A,74, S1654–S1656] to obtain expressions for form factors,P(q), for polydisperse spherical vesicles with various forms of membrane scattering length density (SLD) profile. The SFF approximation is tested against exact form factors that have been numerically integrated over the size distribution, and is shown to represent the vesicle form factor accurately for typical vesicle sizes and membrane thicknesses. Finally, various model SLD profiles are used with the SFF approximation to fit experimental small-angle neutron scattering (SANS) curves from extruded unilamellar vesicles.

The study on the dynamical correlation function,G(r, t), of liquid germanium

2013 ◽  
Vol 53 (4) ◽  
pp. 429-434
Author(s):  
Y. Kato ◽  
Y. Kawakita ◽  
K. Shibata ◽  
S. Takeda ◽  
W.-C. Pilgrim
Keyword(s):  
Correlation Function ◽  
Dynamical Correlation
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