14,104 research outputs found
Density matrix of a finite sub-chain of the Heisenberg anti-ferromagnet
We consider a finite sub-chain on an interval of the infinite XXX model in
the ground state. The density matrix for such a subsystem was described in our
previous works for the model with inhomogeneous spectral parameters. In the
present paper, we give a compact formula for the physically interesting case of
the homogeneous model.Comment: 6 pages, some formulas are refine
Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States
We generalize the results of [Comm. Math. Phys. 299 (2010), 825-866,
arXiv:0911.3731] (hidden Grassmann structure IV) to the case of excited states
of the transfer matrix of the six-vertex model acting in the so-called
Matsubara direction. We establish an equivalence between a scaling limit of the
partition function of the six-vertex model on a cylinder with quasi-local
operators inserted and special boundary conditions, corresponding to
particle-hole excitations, on the one hand, and certain three-point correlation
functions of conformal field theory (CFT) on the other hand. As in hidden
Grassmann structure IV, the fermionic basis developed in previous papers and
its conformal limit are used for a description of the quasi-local operators. In
paper IV we claimed that in the conformal limit the fermionic creation
operators generate a basis equivalent to the basis of the descendant states in
the conformal field theory modulo integrals of motion suggested by A.
Zamolodchikov (1987). Here we argue that, in order to completely determine the
transformation between the above fermionic basis and the basis of descendants
in the CFT, we need to involve excitations. On the side of the lattice model we
use the excited-state TBA approach. We consider in detail the case of the
descendant at level 8
Optimized Neural Networks to Search for Higgs Boson Production at the Tevatron
An optimal choice of proper kinematical variables is one of the main steps in
using neural networks (NN) in high energy physics. Our method of the variable
selection is based on the analysis of a structure of Feynman diagrams
(singularities and spin correlations) contributing to the signal and background
processes. An application of this method to the Higgs boson search at the
Tevatron leads to an improvement in the NN efficiency by a factor of 1.5-2 in
comparison to previous NN studies.Comment: 4 pages, 4 figures, partially presented in proceedings of ACAT'02
conferenc
Emptiness Formation Probability and Quantum Knizhnik-Zamolodchikov Equation
We consider the one-dimensional XXX spin 1/2 Heisenberg antiferromagnet at
zero temperature and zero magnetic field. We are interested in a probability of
formation of a ferromagnetic string in the antiferromagnetic ground-state. We
call it emptiness formation probability [EFP]. We suggest a new technique for
computation of EFP in the inhomogeneous case. It is based on quantum
Knizhnik-Zamolodchikov equation. We evalauted EFP for strings of the length six
in the inhomogeneous case. The homogeneous limit confirms our hypothesis about
the relation of quantum correlations to number theory. We also make a
conjecture about a general structure of EFP for arbitrary lenght of the string
\.Comment: LATEX file, 23 pages, 21 reference
Gauge invariant decomposition of 1-loop multiparticle scattering amplitudes
A simple algorithm is presented to decompose any 1-loop amplitude for
scattering processes of the class 2 fermions -> 4 fermions into a fixed number
of gauge-invariant form factors. The structure of the amplitude is simpler than
in the conventional approaches and its numerical evaluation is made faster. The
algorithm can be efficiently applied also to amplitudes with several thousands
of Feynman diagrams.Comment: 6 page
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