Method for calculating finite size corrections in Bethe ansatz systems: Heisenberg chain and six-vertex model

Vega, H. J. de; Woynarovich, F.

doi:10.1016/0550-3213(85)90271-8

Cited by 228 publications

(157 citation statements)

References 5 publications

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“…These extensive calculations [24,25,26,27,28,29,30,7,31,17,32,8] give very strong and direct evidence to support the predictions of conformal and modular invariance.…”

Section: Finite-size Correctionsmentioning

confidence: 83%

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

Zhou

Pearce

1995

Nuclear Physics B

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“…These extensive calculations [24,25,26,27,28,29,30,7,31,17,32,8] give very strong and direct evidence to support the predictions of conformal and modular invariance.…”

Section: Finite-size Correctionsmentioning

confidence: 83%

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

Zhou

Pearce

1995

Nuclear Physics B

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“…From Equation (48) it is easy to see, that the ground state of the theory lies in the κ = 0 sector, which gives c = 1, the usual central charge for a periodic XXZ spin chain [18,35].…”

Section: Conformal Properties Of Lattice Liouville Theorymentioning

confidence: 99%

“…The thermodynamics [14] and finite size effects [18,19,20,21] of the Bethe Ansatz of the fundamental spin + 1 2 representation of XXZ-chains have been widely discussed in the literature. 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).…”

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

confidence: 99%

“…The finite size corrections of six-vertex models and the corresponding conformal properties have been extensively studied in the literature [18,19,20,21]. For the sixvertex model with an extra phase factor of the form (41), and string exitations, the finite size corrections were calculated by Karowski [19].…”

Section: Finite Size Corrections For the Six-vertex Modelmentioning

confidence: 99%

“…Based on this, systematic methods for analytical calculation of the finite size corrections have been developed [18,19,20,21]. For a spin chain or lattice model, the finite size analysis yields 1 N corrections to the eigenvalues of the transfer matrix, where N is the number of lattice sites.…”

Section: Introductionmentioning

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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Free energy and correlation lengths of quantum chains related to restricted solid‐on‐solid lattice models

Klümper¹

1992

Annalen der Physik

157

287

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An approach is presented for calculating the free energy as well as the correlation lengths of integrable quantum chains at arbitrary finite temperatures. The method is applied to critical Hamiltonians related to restricted solid-on-olid models comprising the hierarchy by Andrews, Baxter and Forrester, and generalizations hereof by the fusion procedure. The derived non-linear integral equations can be studied analytically in the low-temperature and high-temperature limits. The central charges and all primary conformal weights are obtained for the generalized minimal unitary series of conformal field theory and the Z , parafermion theories. Thus an extension of the thermodynamic Bethe Ansatz is realized which recently has been speculated on in the literature.

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Method for calculating finite size corrections in Bethe ansatz systems: Heisenberg chain and six-vertex model

Cited by 228 publications

References 5 publications

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

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

Connections of the Liouville model and XXZ spin chain

Free energy and correlation lengths of quantum chains related to restricted solid‐on‐solid lattice models

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