On Cherednik and Nazarov-Sklyanin large N limit construction for integrable many-body systems with elliptic dependence on momenta

Grekov, A.; Zotov, A.

doi:10.1007/jhep12(2021)062

Cited by 3 publications

(1 citation statement)

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“…Overview of Quantum DELL System. First we review the basics of the quantum double elliptic system which was discovered by two of the authors [KS] and further developed in [GZ2,GZ]. (see also [BMMM,MM,AMMZ,ABM + ,AMM,AMM2,FGNR,BGOR] for different approach to double elliptic models).…”

Section: The Dell Systemmentioning

confidence: 99%

Double Inozemtsev Limits of the Quantum DELL System

Gorsky,

Koroteev,

Koroteeva

et al. 2021

Preprint

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In this letter we study various Inozemtsev-type limits of the quantum double elliptic (DELL) system when both elliptic parameters are sent to zero at different rates, while the coupling constant is sent to infinity, such that a certain combination of the three parameters is kept fixed. We find a regime in which such double Inozemtsev limit of DELL produces the elliptic Ruijsenaars-Schneider (eRS) Hamiltonians albeit in an unconventional normalization. We discuss other double scaling limits and anisotropic scaling of coordinates and momenta. In addition we provide a formal expression for the eigenvalues of the eRS Hamiltonians solely in terms of their eigenfunctions.

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Section: The Dell Systemmentioning

confidence: 99%

Double Inozemtsev Limits of the Quantum DELL System

Gorsky,

Koroteev,

Koroteeva

et al. 2021

Preprint

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Dualities in quantum integrable many-body systems and integrable probabilities. Part I

Gorsky

Vasilyev

Zotov

2022

J. High Energ. Phys.

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In this study we map the dualities observed in the framework of integrable probabilities into the dualities familiar in a realm of integrable many-body systems. The dualities between the pairs of stochastic processes involve one representative from Macdonald-Schur family, while the second representative is from stochastic higher spin six-vertex model of TASEP family. We argue that these dualities are counterparts and generalizations of the familiar quantum-quantum (QQ) dualities between pairs of integrable systems. One integrable system from QQ dual pair belongs to the family of inhomogeneous XXZ spin chains, while the second to the Calogero-Moser-Ruijsenaars-Schneider (CM-RS) family. The wave functions of the Hamiltonian system from CM-RS family are known to be related to solutions to (q)KZ equations at the inhomogeneous spin chain side. When the wave function gets substituted by the measure, bilinear in wave functions, a similar correspondence holds true. As an example, we have elaborated in some details a new duality between the discrete-time inhomogeneous multispecies TASEP model on the circle and the quantum Goldfish model from the RS family. We present the precise map of the inhomogeneous multispecies TASEP and 5-vertex model to the trigonometric and rational Goldfish models respectively, where the TASEP local jump rates get identified as the coordinates in the Goldfish model. Some comments concerning the relation of dualities in the stochastic processes with the dualities in SUSY gauge models with surface operators included are made.

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On the status of DELL systems

Mironov,

Morozov

2024

Nuclear Physics B

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On Cherednik and Nazarov-Sklyanin large N limit construction for integrable many-body systems with elliptic dependence on momenta

Cited by 3 publications

References 50 publications

Double Inozemtsev Limits of the Quantum DELL System

Double Inozemtsev Limits of the Quantum DELL System

Dualities in quantum integrable many-body systems and integrable probabilities. Part I

On the status of DELL systems

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