Solution of functional equations of restricted An−1(1) fused lattice models

Zhou, Yingyu; Pearce, Paul A.

doi:10.1016/0550-3213(95)00210-j

Cited by 18 publications

(28 citation statements)

References 48 publications

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“…There could be interesting applications of our method to conformal QFT's in two dimensions if we consider them as some limiting cases of massive theories. These limiting cases could be the ultraviolet limit of a small volume L → ∞ (see for example [14]) or analytic continuation w.r.t. the number of components of a field, like in [51], or something else.…”

Section: Discussionmentioning

confidence: 99%

Finite volume spectrum of 2D field theories from Hirota dynamics

Gromov

Казаков

Vieira

2009

J. High Energy Phys.

162

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We propose, using the example of the O(4) sigma model, a general method for solving integrable two dimensional relativistic sigma models in a finite size periodic box. Our starting point is the so-called Y-system, which is equivalent to the thermodynamic Bethe ansatz equations of Yang and Yang. It is derived from the Zamolodchikov scattering theory in the cross channel, for virtual particles along the non-compact direction of the space-time cylinder. The method is based on the integrable Hirota dynamics that follows from the Y-system. The outcome is a nonlinear integral equation for a single complex function, valid for an arbitrary quantum state and accompanied by the finite size analogue of Bethe equations. It is close in spirit to the Destri-deVega (DdV) equation. We present the numerical data for the energy of various states as a function of the size, and derive the general Lüscher-type formulas for the finite size corrections. We also re-derive by our method the DdV equation for the SU (2) chiral Gross-Neveu model.

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Section: Discussionmentioning

confidence: 99%

Finite volume spectrum of 2D field theories from Hirota dynamics

Gromov

Казаков

Vieira

2009

J. High Energy Phys.

162

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“…In particular, the long distance behavior of this type of models has been studied by many methods (see for instance [16,17,18]). For |n| > 2 the spectrum has a gap and the correlation length is finite.…”

Section: Results and Conclusionmentioning

confidence: 99%

Algebraic Bethe ansatz for the FPL²model

Jacobsen¹,

Zinn-Justin²

2004

J. Phys. A: Math. Gen.

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An exact solution of the model of fully packed loops of two colors on a square lattice has recently been proposed by Dei Cont and Nienhuis using the coordinate Bethe Ansatz approach. We point out here a simpler alternative, in which the transfer matrix is directly identified as a product of R-matrices; this allows to apply the (nested) algebraic Bethe Ansatz, which leads to the same Bethe equations. We comment on some of the applications of this result. 02/2004

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“…A systematic derivation of the T -and Y -systems for all excitations in the context of sℓ(2) RSOS models was obtained in 1992 by Klümper and Pearce [41]. Generalizations of T -and Y -systems to higher-rank models, including models with sℓ(3) symmetry, are considered in [42,43,29,44]. The T -and Y -systems for the sℓ(2) logarithmic minimal loop models were obtained in [45].…”

Section: Introductionmentioning

confidence: 99%

“…The precise form of these closed equations strongly resembles those of the related so-called complex su(3) Toda theory [24]. In strong contrast, for the A (1) 2 RSOS models, the known Y -systems [29] truncate at a finite level. The actual solution of the universal A…”

Section: Introductionmentioning

confidence: 99%

Fusion hierarchies, $T$-systems and $Y$-systems for the $A_2^{(1)}$ models

Morin-Duchesne,

Pearce,

Rasmussen

2018

Preprint

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The family of A(1) 2 models on the square lattice includes a dilute loop model, a 15-vertex model and, at roots of unity, a family of RSOS models. The fused transfer matrices of the general loop and vertex models are shown to satisfy sℓ(3)-type fusion hierarchies. We use these to derive explicit T -and Ysystems of functional equations. At roots of unity, we further derive closure identities for the functional relations and show that the universal Y -system closes finitely. The A (1) 2 RSOS models are shown to satisfy the same functional and closure identities but with finite truncation.

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Solution of functional equations of restricted An−1(1) fused lattice models

Abstract: Functional equations, in the form of fusion hierarchies, are studied for the transfer matrices of the fused restricted A

Cited by 18 publications

References 48 publications

Finite volume spectrum of 2D field theories from Hirota dynamics

Finite volume spectrum of 2D field theories from Hirota dynamics

Algebraic Bethe ansatz for the FPL²model

Fusion hierarchies, $T$-systems and $Y$-systems for the $A_2^{(1)}$ models

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Solution of functional equations of restricted An−1(1) fused lattice models

Abstract: Functional equations, in the form of fusion hierarchies, are studied for the transfer matrices of the fused restricted A

Cited by 18 publications

References 48 publications

Finite volume spectrum of 2D field theories from Hirota dynamics

Finite volume spectrum of 2D field theories from Hirota dynamics

Algebraic Bethe ansatz for the FPL2model

Fusion hierarchies, $T$-systems and $Y$-systems for the $A_2^{(1)}$ models

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Algebraic Bethe ansatz for the FPL²model