Common structures between finite systems and conformal field theories through quantum groups

Pasquier, Vincent; Saleur, Hubert

doi:10.1016/0550-3213(90)90122-t

Cited by 728 publications

(1,006 citation statements)

References 17 publications

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“…We remark here that the e j admit a representation in terms of Pauli spin matrices. In that representation, the Hamiltonian (6) becomes that of the quantum XXZ spin chain with diagonal boundaries [39]. This model is integrable and quantities such as the conformal scaling exponents can be calculated exactly, for example using Bethe Ansatz techniques [8].…”

Section: Rsos Loop and Six-vertex Correspondencementioning

confidence: 99%

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The Raise and Peel Model of a Fluctuating Interface

Gier

Nienhuis

Pearce

et al. 2004

Journal of Statistical Physics

133

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We propose a one-dimensional nonlocal stochastic model of adsorption and desorption depending on one parameter, the adsorption rate. At a special value of this parameter, the model has some interesting features. For example, the spectrum is given by conformal field theory, and the stationary non-equilibrium probability distribution is given by the two-dimensional equilibrium distribution of the ice model with domain wall type boundary conditions. This connection is used to find exact analytic expressions for several quantities of the stochastic model. Vice versa, some understanding of the ice model with domain wall type boundary conditions can be obtained by the study of the stochastic model. At the special point we study several properties of the model, such as the height fluctuations as well as cluster and avalanche distributions. The latter has a long tail which shows that the model exhibits self organized criticality. We also find in the stationary state a special phase transition without enhancement and with a crossover exponent φ = 2/3. Furthermore, we study the phase diagram of the model as a function of the adsorption rate and find two massive phases and a scale invariant phase where conformal invariance is broken.

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Section: Rsos Loop and Six-vertex Correspondencementioning

confidence: 99%

“…As shown in [60] its spectrum is given by the characters of a c = 0 LCFT. The same Hamiltonian corresponds to a sector of the XXZ quantum chain with quantum group boundary conditions [39]. The first motivation in our study was to see the specific features of a stochastic model in which one has LCFT.…”

Section: Conlusionsmentioning

confidence: 99%

The Raise and Peel Model of a Fluctuating Interface

Gier

Nienhuis

Pearce

et al. 2004

Journal of Statistical Physics

133

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“…P R is a projection operator onto Young Diagrams, and orthogonality of these projectors allowed one to diagonalize the two-point functions. One of the interesting features of physical applications of quantum groups at roots of unity is that they capture vanishing properties of correlation functions or fusion rules [33][34] [36]. It will be interesting to look for signatures of such vanishings in this context.…”

Section: Correlators As Traces Of Quantum Group Generatorsmentioning

confidence: 99%

“…Physical applications of quantum groups in two-dimensional CFT and three dimensional Chern Simons theory [33,34,35,36,37] show that, in addition to the quantum coproduct an interesting role is played by quantum traces. In the Mathematics literature quantum traces with different choices of Cartan elements have been shown to have interesting properties [38].…”

Section: Introductionmentioning

confidence: 99%

Strings on plane waves, super-Yang–Mills in four dimensions, quantum groups at roots of one

Corley

Ramgoolam

2004

Nuclear Physics B

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We show that the BMN operators in D = 4 N = 4 super Yang Mills theory proposed as duals of stringy oscillators in a plane wave background have a natural quantum group construction in terms of the quantum deformation of the SO(6) R symmetry. We describe in detail how a q-deformed U (2) subalgebra generates BMN operators, with q ∼ e 2iπ J . The standard quantum co-product as well as generalized traces which use q-cyclic operators acting on tensor products of Higgs fields are the ingredients in this construction. They generate the oscillators with the correct ( undeformed ) permutation symmetries of Fock space oscillators. The quantum group can be viewed as a spectrum generating algebra, and suggests that correlators of BMN operators should have a geometrical meaning in terms of spaces with quantum group symmetry.

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“…The constructions of the quantum group invariant spin systems [30] uses the RE [31,32,42,54]. Recent field theoretical applications of the RE can be found in [23][24][25][26][27]36].…”

Section: Reflection Equations and Their Covariancementioning

confidence: 99%

Yang-Baxter equation and reflection equations in integrable models

Kulish

1996

Low-Dimensional Models in Statistical Physics and Quantum Field Theory

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The definitions of the main notions related to the quantum inverse scattering methods are given. The Yang-Baxter equation and reflection equations are derived as consistency conditions for the factorizable scattering on the whole line and on the half-line using the ZamolodchikovFaddeev algebra. Due to the vertex-IRF model correspondence the face model analogue of the ZF-algebra and the IRF reflection equation are written down as well as the Z 2 -graded and colored algebra forms of the YBE and RE.

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Common structures between finite systems and conformal field theories through quantum groups

Cited by 728 publications

References 17 publications

The Raise and Peel Model of a Fluctuating Interface

The Raise and Peel Model of a Fluctuating Interface

Strings on plane waves, super-Yang–Mills in four dimensions, quantum groups at roots of one

Yang-Baxter equation and reflection equations in integrable models

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