Connecting Lattice and Relativistic Models via Conformal Field Theory

Boos, H.; Korepin, V. E.; Смирнов, Ф.

doi:10.1007/3-7643-7341-5_5

Cited by 9 publications

(9 citation statements)

References 21 publications

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“…6) We remark that at ∆ = 1 our results reproduce the same values as in [23,26]. It is immediate to see them from the following asymptotic expansions at η = 0: Table 1: Exact values of the third-neighbor correlation functions at several points of ∆.…”

Section: The Third-neighbor Correlation Functions and Some Other Corrsupporting

confidence: 82%

“…Actually, a few years ago, Boos et al succeeded in simplifying the multiple integrals for EFP at ∆ = 1. They could express the EFP up to m = 6 as polynomials with respect to the specific values of ζ function [22][23][24][25]. The same method was applied to the third-neighbor correlations at 1 Note that such a program has been achieved for the asymptotic behavior of the EFP P (m) at ∆ = 1/2.…”

mentioning

confidence: 99%

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Third-neighbour and other four-point correlation functions of spin-1/2XXZchain

Kato¹,

Shiroishi²,

Takahashi³

et al. 2004

J. Phys. A: Math. Gen.

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The correlation functions of the spin-1/2 XXZ chain in the ground state were expressed in the form of multiple integrals for −1 < ∆ ≤ 1 and 1 < ∆. In particular, adjacent four-point correlation functions were given as certain four-dimensional integrals. We show that these integrals can be reduced to polynomials with respect to specific one-dimensional integrals. The results give the polynomial representation of the third-neighbor correlation functions.

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Section: The Third-neighbor Correlation Functions and Some Other Corrsupporting

confidence: 82%

mentioning

confidence: 99%

Third-neighbour and other four-point correlation functions of spin-1/2XXZchain

Kato¹,

Shiroishi²,

Takahashi³

et al. 2004

J. Phys. A: Math. Gen.

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“…However the rational functions f n,I,J were not described. In [6], it was explained that a similar formula continues to hold for the correlation functions of quantum group reduction of the XXZ model.…”

Section: Introductionmentioning

confidence: 85%

Reduced qKZ Equation and Correlation Functions of the XXZ Model

Boos

Jimbo

Miwa

et al. 2005

Commun. Math. Phys.

122

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Abstract. Correlation functions of the XXZ model in the massive and massless regimes are known to satisfy a system of linear equations. The main relations among them are the difference equations obtained from the qKZ equation by specializing the variables (λ 1 , · · · , λ 2n ) as (λ 1 , · · · , λ n , λ n + 1, · · · , λ 1 + 1). We call it the reduced qKZ equation. In this article we construct a special family of solutions to this system. They can be written as linear combinations of products of two transcendental functionsω, ω with coefficients being rational functions. We show that correlation functions of the XXZ model in the massive regime are given by these formulas with an appropriate choice ofω, ω. We also present a conjectural formula in the massless regime.

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“…A similar function was first obtained in [17] in a different representation 9 , and was used in a very different context in [26]. We present it here in what we believe to be a simpler expression.…”

Section: Generalizationsmentioning

confidence: 81%

Form factors in the massless coset models

Grinza

Ponsot

2005

Nuclear Physics B

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IntroductionThe general problem of finding a suitable description of Renormalization Group (RG) flows between different non-trivial critical point in Quantum Field Theory is an open and appealing problem. In this respect 2d integrable QFTs provide a privileged framework where there is the actual possibility of finding a detailed description of such flows. As a matter of fact, one of the remarkable consequences of integrability is the knowledge of the exact S-matrix which allows to calculate exact form-factors [1][2][3]. From the latter one can reconstruct correlators by means of the spectral expansion which provides a non-perturbative representation of them. Such a representation has often been very accurate in the past -though it was noticed some time ago in [4] that this common belief, even for massive theories, is too optimistic in general-and allows, for example, to recover the conformal data using the c-theorem sum rule [5,6] which gives the difference between the central charges of the UV and IR fixed points. Integrable RG flows which limit in the infrared is a non-trivial CFT can be described by massless excitations, for which an exact scattering matrix can be found. More precisely, we deal with right and left movers and three different types of scatterings, associated to right-right, left-left, and right-left interactions. The right-right and left-left S-matrices, whose definition is formal, are independent of the RG scale, and are solely characterized by the properties of the IR fixed point CFT. On the contrary, the right-left scattering is quite rigorously defined [7]. It becomes trivial in the IR limit, thus the left and right movers decouple, and we obtain the IR CFT. In [8], using the S-matrix proposed in [7], a few form-factors 3 of some local and non local operators were constructed for the simplest model describing the flow [9][10][11] between the Tricritical Ising model (TIM) and the Ising model (IM), where the supersymmetry is spontaneously broken. Remarkably enough, the numerical results performed in [8] show that the knowledge of the form-factor with the lowest number of intermediate particles is enough to give quite an accurate approximation for the correlation function at almost all RG scale. Of course it is desirable to figure out whether these spectacular features remain valid in less trivial massless flows. In this respect, one has to take into account results obtained recently in [12] about the calculation of form factors in a massive integrable model of QFT called the SS model [13], as well as in its RSOS restrictions. The numerical checks performed in [12] show in particular the two-particles approximation of the c-theorem sum rule fails to give the usual good approximation of the exact results, showing instead large discrepancies (about 20-25%, see below).In this article we will consider the construction of form factors of the trace operator for an arbitrary number of intermediate particles in the family of massless flows [14] between the UV coset models [15] su(2) k+1 ⊗ su(2) k /su(...

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Connecting Lattice and Relativistic Models via Conformal Field Theory

Cited by 9 publications

References 21 publications

Third-neighbour and other four-point correlation functions of spin-1/2XXZchain

Third-neighbour and other four-point correlation functions of spin-1/2XXZchain

Reduced qKZ Equation and Correlation Functions of the XXZ Model

Form factors in the massless coset models

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