TRIGONOMETRIC sℓ(2) GAUDIN MODEL WITH BOUNDARY TERMS

António, N. Cirilo; Manojlović, N.; Nagy, Zoltán

doi:10.1142/s0129055x13430046

Cited by 12 publications

(7 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Thus, to obtain the twisted-periodic transfer matrix (19) from the attenuated limit (18) of the boundary transfer matrix (11), we need to impose that γ depends on N :…”

Section: L=1mentioning

confidence: 99%

“…The transfer matrix (11) in the rational limit, particularly in the form (17), is readily obtained by employing the expressions ( 23), ( 24) and ( 25) above. To then determine the attenuated limit of this rational transfer matrix, we first observe that from (23) above, Ľ(u) → I as u → ∞.…”

Section: Rational Limitmentioning

confidence: 99%

“…The quasi-classical limit of the Boundary Quantum Inverse Scattering Method was studied by Sklyanin in [38], prior to his more well-known publication [39]. Adopting this approach, several authors have implemented constructions to produce generalised versions of Richardson-Gaudin systems [11,12,21,41,43]. In-depth analyses however, including implications for formulating new pairing Hamiltonians, appear to be have not been widely undertaken.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the boundaries of quantum integrability for the spin-1/2 Richardson–Gaudin system

2014

View full text Add to dashboard Cite

We discuss a generalised version of Sklyanin's Boundary Quantum Inverse Scattering Method applied to the spin-1/2, trigonometric sl(2) case, for which both the twisted-periodic and boundary constructions are obtained as limiting cases. We then investigate the quasi-classical limit of this approach leading to a set of mutually commuting conserved operators which we refer to as the trigonometric, spin-1/2 Richardson-Gaudin system. We prove that the rational limit of the set of conserved operators for the trigonometric system is equivalent, through a change of variables, rescaling, and a basis transformation, to the original set of trigonometric conserved operators. Moreover we prove that the twisted-periodic and boundary constructions are equivalent in the trigonometric case, but not in the rational limit.1 The elliptic case is generally not considered. It breaks u(1) symmetry leading to non-conservation of particle number.

show abstract

“…Thus, to obtain the twisted-periodic transfer matrix (19) from the attenuated limit (18) of the boundary transfer matrix (11), we need to impose that γ depends on N :…”

Section: L=1mentioning

confidence: 99%

Section: Rational Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the boundaries of quantum integrability for the spin-1/2 Richardson–Gaudin system

2014

View full text Add to dashboard Cite

show abstract

“…Let us also mention that the algebraic Bethe ansatz was already applied to solve open Gaudin model using the vertex-IRF correspondence of the XXZ spin chain [26,43]. However, as pointed in [14], the model considered in [26,43] is obtained as a limit from the XXZ spin chain and is different of the one studied here which is constructed directly from a classical r-matrix.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary

Crampé¹

2017

SIGMA

View full text Add to dashboard Cite

Abstract. We solve the XXZ Gaudin model with generic boundary using the modified algebraic Bethe ansatz. The diagonal and triangular cases have been recovered in this general framework. We show that the model for odd or even lengths has two different behaviors. The corresponding Bethe equations are computed for all the cases. For the chain with even length, inhomogeneous Bethe equations are necessary. The higher spin Gaudin models with generic boundary is also treated.

show abstract

“…В общем случае при изучении спиновой цепочки эти условия нормировки не так существенны. Однако они обеспечивают квазиклассическое разложение трансферматрицы, что приводит к соответствующим гамильтонианам Годена с граничными членами [40], [42].…”

Section: Introductionunclassified

Жорданова деформация открытой $s\ell(2)$-модели Годена

Антонио¹,

António²,

Манойлович³

et al. 2014

ТМФ

View full text Add to dashboard Cite

Получена деформированная sℓ(2)-модель Годена с граничными условиями, сохраняющими интегрируемость. На основании жордановой деформации SL(2)-инвариантной R-матрицы Янга и общих решений ассоциированного уравнения отражения и дуального уравнения отражения получена соответствующая неоднородная XXX-цепочка спина 1/2. Квазиклассическое разложение трансферматрицы приводит к деформированным sℓ(2)-гамильтонианам Годена с граничными членами. Ключевые слова: точно решаемые модели, модель Годена.

show abstract

TRIGONOMETRIC sℓ(2) GAUDIN MODEL WITH BOUNDARY TERMS

Cited by 12 publications

References 43 publications

On the boundaries of quantum integrability for the spin-1/2 Richardson–Gaudin system

On the boundaries of quantum integrability for the spin-1/2 Richardson–Gaudin system

Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary

Жорданова деформация открытой $s\ell(2)$-модели Годена

Contact Info

Product

Resources

About