Quantum toroidal gl1 and Bethe ansatz

B. Feigin; M. Jimbo; T. Miwa; E. Mukhin

doi:10.1088/1751-8113/48/24/244001

Quantum toroidal gl₁ and Bethe ansatz

B. Feigin, M. Jimbo, T. Miwa, E. Mukhin

Research output: Contribution to journal › Article › peer-review

Abstract

We establish the method of Bethe ansatz for the XXZ type model obtained from the R matrix associated to quantum toroidal gl₁. We do this by using shuffle realizations of the modules and by showing that the Hamiltonian of the model is obtained from a simple multiplication operator by taking an appropriate quotient. We expect this approach to be applicable to a wide variety of models.

Original language	English
Article number	244001
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	48
Issue number	24
DOIs	https://doi.org/10.1088/1751-8113/48/24/244001
State	Published - 19 Jun 2015
Externally published	Yes

Keywords

Bethe ansatz
quantum toroidal algebra
shuffle algebra

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability
Modelling and Simulation
Mathematical Physics
General Physics and Astronomy

Access to Document

10.1088/1751-8113/48/24/244001

Cite this

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title = "Quantum toroidal gl1 and Bethe ansatz",

abstract = "We establish the method of Bethe ansatz for the XXZ type model obtained from the R matrix associated to quantum toroidal gl1. We do this by using shuffle realizations of the modules and by showing that the Hamiltonian of the model is obtained from a simple multiplication operator by taking an appropriate quotient. We expect this approach to be applicable to a wide variety of models.",

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AU - Jimbo, M.

AU - Miwa, T.

AU - Mukhin, E.

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Y1 - 2015/6/19

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AB - We establish the method of Bethe ansatz for the XXZ type model obtained from the R matrix associated to quantum toroidal gl1. We do this by using shuffle realizations of the modules and by showing that the Hamiltonian of the model is obtained from a simple multiplication operator by taking an appropriate quotient. We expect this approach to be applicable to a wide variety of models.

KW - Bethe ansatz

KW - quantum toroidal algebra

KW - shuffle algebra

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DO - 10.1088/1751-8113/48/24/244001

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