Cylinder partition function of the 6-vertex model from algebraic geometry

Bajnok, Zoltán; Jacobsen, Jesper Lykke; Jiang, Yunfeng; Nepomechie, Rafael I.; Zhang, Yang

doi:10.1007/jhep06(2020)169

Cited by 14 publications

(15 citation statements)

References 55 publications

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“…For this state the overlap can be written as (the number of magnons has to equal to the half length of the spin chain i.e. N = 2M ) [33] | Dimer |y,…”

Section: Overlaps In Su(2|2) C Spin Chainsmentioning

confidence: 99%

Boundary states, overlaps, nesting and bootstrapping AdS/dCFT

Gombor

Bajnok

2020

J. High Energ. Phys.

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Integrable boundary states can be built up from pair annihilation amplitudes called K-matrices. These amplitudes are related to mirror reflections and they both satisfy Yang Baxter equations, which can be twisted or untwisted. We relate these two notions to each other and show how they are fixed by the unbroken symmetries, which, together with the full symmetry, must form symmetric pairs. We show that the twisted nature of the K-matrix implies specific selection rules for the overlaps. If the Bethe roots of the same type are paired the overlap is called chiral, otherwise it is achiral and they correspond to untwisted and twisted K-matrices, respectively. We use these findings to develop a nesting procedure for K-matrices, which provides the factorizing overlaps for higher rank algebras automatically. We apply these methods for the calculation of the simplest asymptotic all-loop 1-point functions in AdS/dCFT. In doing so we classify the solutions of the YBE for the K-matrices with centrally extended $$ \mathfrak{su} $$ su (2|2)c symmetry and calculate the generic overlaps in terms of Bethe roots and ratio of Gaudin determinants.

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“…For this state the overlap can be written as (the number of magnons has to equal to the half length of the spin chain i.e. N = 2M ) [33] | Dimer |y,…”

Section: Overlaps In Su(2|2) C Spin Chainsmentioning

confidence: 99%

Boundary states, overlaps, nesting and bootstrapping AdS/dCFT

Gombor

Bajnok

2020

J. High Energ. Phys.

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“…ingredients in the context of quantum quenches, partition functions of integrable lattice models [3], as well as the weak coupling limit of integrability in AdS/CFT [4][5][6].…”

Section: Jhep06(2020)022mentioning

confidence: 99%

On exact overlaps in integrable spin chains

Jiang

Pozsgay

2020

J. High Energ. Phys.

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We compute the exact overlaps between integrable boundary states and onshell Bethe states for integrable spin chains. Our method is based on the coordinate Bethe Ansatz and does not rely on the "rotation trick" of the corresponding lattice model. It leads to a rigorous proof of the factorized overlap formulae in a number of cases, some of which were hitherto inaccessible to earlier methods. As concrete examples, we consider the compact XXX and XXZ Heisenberg spin chains, and the non-compact SL(2, R) spin chain.

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“…However, contrary to the XXX case, the order of Q 1,1 is the same as that of Q. 6 Since the QQ-equations for the XXZ case (3.8) are the same as for the XXX case (2.13), the solutions are the same, too. In particular, formulas such as (2.18)-(2.20) are exactly the same, and polynomiality of Q 0,1 is equivalent to the polynomiality of T , which gives the BA equations (3.5).…”

Section: Jhep03(2020)177mentioning

confidence: 96%

“…The purpose of this paper is to generalize the SU(2)invariant Q-system [3] in two different directions: from rational to trigonometric, and from closed to open. These new Q-systems will be used to compute partition functions for trigonometric vertex models and for vertex models with boundaries [6,7].…”

Section: Jhep03(2020)177mentioning

confidence: 99%