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H. E. Boos

Publications and source records attributed to H. E. Boos.

11 recordsLinked to original sources
arXiv2005

First principle approach to correlation functions of spin-1/2 Heisenberg chain : fourth-neighbor correlators

We show how correlation functions of the spin-1/2 Heisenberg chain without magnetic field in the anti-ferromagnetic ground state can be explicitly calculated using information contained in the quantum Knizhnik-Zamolodchikov equation [qKZ]. We find several fundamental relations which the inhomogeneous correlations should fulfill. On the other hand, it turns out that these relations can fix the form of the correlations uniquely. Actually, applying this idea, we have obtained all the correlation functions on five sites. Particularly by taking the homogeneous limit, we have got the analytic form of the fourth-neighbor pair correlator < S_j^z S_{j+4}^z >.

hep-th↗
arXiv2003

Connecting lattice and relativistic models via conformal field theory

We consider the quantum group invariant XXZ-model. In infrared limit it describes Conformal Field Theory with modified energy-momentum tensor. The correlation functions are related to solutions of level -4 of qKZ equations. We describe these solutions relating them to level 0 solutions. We further consider general matrix elements (form factors) containing local operators and asymptotic states. We explain that the formulae for solutions of qKZ equations suggest a decomposition of these matrix elements with respect to states of corresponding Conformal Field Theory .

math-ph↗
arXiv2002

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 \.

hep-th↗
arXiv2002

Quantum Correlations and Number Theory

We study spin-1/2 Heisenberg XXX antiferromagnet. The spectrum of the Hamiltonian was found by Hans Bethe in 1931. We study the probability of formation of ferromagnetic string in the antiferromagnetic ground state, which we call emptiness formation probability P(n). This is the most fundamental correlation function. We prove that for the short strings it can be expressed in terms of the Riemann zeta function with odd arguments, logarithm ln 2 and rational coefficients. This adds yet another link between statistical mechanics and number theory. We have obtained an analytical formula for P(5) for the first time. We have also calculated P(n) numerically by the Density Matrix Renormalization Group. The results agree quite well with the analytical ones. Furthermore we study asymptotic behavior of P(n) at finite temperature by Quantum Monte-Carlo simulation. It also agrees with our previous analytical results.

cond-mat.stat-mech↗
arXiv2001

Quantum Spin Chains and Riemann Zeta Function with Odd Arguments

Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model. We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in thermodynamics limit. We prove that for short strings the probability can be expressed in terms of Riemann zeta function with odd arguments.

hep-th↗
arXiv1999

Bethe ansatz for the three-layer Zamolodchikov model

This paper is a continuation of our previous work (solv-int/9903001). We obtain two more functional relations for the eigenvalues of the transfer matrices for the $sl(3)$ chiral Potts model at $q^2=-1$. This model, up to a modification of boundary conditions, is equivalent to the three-layer three-dimensional Zamolodchikov model. From these relations we derive the Bethe ansatz equations.

solv-int↗
arXiv1999

Functional relations and nested Bethe ansatz for sl(3) chiral Potts model at q^2=-1

We obtain the functional relations for the eigenvalues of the transfer matrix of the sl(3) chiral Potts model for q^2=-1. For the homogeneous model in both directions a solution of these functional relations can be written in terms of roots of Bethe ansatz-like equations. In addition, a direct nested Bethe ansatz has also been developed for this case.

solv-int↗
arXiv1995

$Psi$ - Vectors for Three Dimensional Models

In this paper we apply the method of psi-vectors to three dimensional statistical models. This method gives the correspondence between the Bazhanov -- Baxter model and its vertex formulation. Considering psi-vectors for the Planar model, we obtain its self-duality.

q-alg↗
arXiv1995

Modified tetrahedron equation and related 3D integrable models,II

This work is a continuation of paper (hep-th/9407146) where the Boltzmann weights for the N-state integrable spin model on the cubic lattice has been obtained only numerically. In this paper we present the analytical formulae for this model in a particular case. Here the Boltzmann weights depend on six free parameters including the elliptic modulus. The obtained solution allows to construct a two-parametric family of the commuting two-layer transfer matrices. Presented model is expected to be simpler for a further investigation in comparison with a more general model mentioned above.

hep-th↗
arXiv1994

Modified Tetrahedron Equations and Related 3D Integrable Models

Using a modified version of the tetrahedron equations we construct a new family of $N$-state three-dimensional integrable models with commuting two-layer transfer-matrices. We investigate a particular class of solutions to these equations and parameterize them in terms of elliptic functions. The corresponding models contain one free parameter $k$ -- an elliptic modulus.

hep-th↗