Local Hamiltonians for integrable quantum models on a lattice

Tarasov, Vitaly; Takhtadzhyan, L. A.; Faddeev, L. D.

doi:10.1007/bf01018648

Cited by 173 publications

(228 citation statements)

References 9 publications

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“…Accordingly it would be a desirable goal to map the spin (− 1 2 ) Liouville Bethe equations (27) to the spin + 1 2 XXZ ones (28). This can be done in the string picture [14] of solutions to the Bethe Ansatz equations.…”

Section: Mapping the Lattice Liouville Model To The Spin 1 2 Xxz Chainmentioning

confidence: 99%

“…Thus L n,a (λ) does not degenerate to a permutation operator at any value of the spectral parameter λ, and it is not good for investigating lattice dynamics. To get an integrable Hamiltonian that generates lattice Liouville dynamics, one would have to introduce fundamental Lax-operators L n,f that intertwine two quantum spaces [28].…”

Section: Mapping the Lattice Liouville Model To The Spin 1 2 Xxz Chainmentioning

confidence: 99%

“…Following [28] one can read off the energy and momentum eigenvalues from the eigenvalues of the diagonal elements A and D of the auxiliary Lax-operators L n,a . The momentum eigenvalues are…”

Section: Mapping the Lattice Liouville Model To The Spin 1 2 Xxz Chainmentioning

confidence: 99%

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Connections of the Liouville model and XXZ spin chain

Faddeev

Tirkkonen

1995

Nuclear Physics B

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The quantum theory of the Liouville model with imaginary field is considered using the Quantum Inverse Scattering Method. An integrable structure with nontrivial spectral parameter dependence is developed for lattice Liouville theory by scaling the L-matrix of lattice sine-Gordon theory. This L-matrix yields Bethe Ansatz equations for Liouville theory, by the methods of the algebraic Bethe Ansatz. Using the string picture of exited Bethe states, the lattice Liouville Bethe equations are mapped to the corresponding spin 1 2 XXZ chain equations. The well developed theory of finite size corrections in spin chains is used to deduce the conformal properties of the lattice Liouville Bethe states. The unitary series of conformal field theories emerge for Liouville couplings of the form γ = π ν ν+1 , corresponding to root of unity XXZ anisotropies. The Bethe states give the full spectrum of the corresponding unitary conformal field theory, with the primary states in the Kač table parameterized by a string length K, and the remnant of the chain length mod (ν + 1). *

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Section: Mapping the Lattice Liouville Model To The Spin 1 2 Xxz Chainmentioning

confidence: 99%

Section: Mapping the Lattice Liouville Model To The Spin 1 2 Xxz Chainmentioning

confidence: 99%

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Connections of the Liouville model and XXZ spin chain

Faddeev

Tirkkonen

1995

Nuclear Physics B

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“…This equation allows to interprete r as a fundamental L-operator of quantum chain [4] and use the machinery of QISM (see e.g. [6]).…”

Section: Integrabilitymentioning

confidence: 99%

Hirota equation as an example of an integrable symplectic map

1994

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“…Expanding the logarithim of the transfer matrix gives the local commuting Hamiltonians [42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Spin models and superconformal Yang–Mills theory

Dolan

Nappi

2005

Nuclear Physics B

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We apply novel techniques in planar superconformal Yang-Mills theory which stress the role of the Yangian algebra. We compute the first two Casimirs of the Yangian, which are identified with the first two local abelian Hamiltonians with periodic boundary conditions, and show that they annihilate the chiral primary states. We streamline the derivation of the R-matrix in a conventional spin model, and extend this computation to the gauge theory. We comment on higher-loop corrections and higher-loop integrability.

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Local Hamiltonians for integrable quantum models on a lattice

Cited by 173 publications

References 9 publications

Connections of the Liouville model and XXZ spin chain

Connections of the Liouville model and XXZ spin chain

Hirota equation as an example of an integrable symplectic map

Spin models and superconformal Yang–Mills theory

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