Quantum Integrable Models and Discrete Classical Hirota Equations

被引：0
|
作者：
I. Krichever
O. Lipan
P. Wiegmann
A. Zabrodin
机构：
[1] Department of Mathematics,
[2] Columbia University,undefined
[3] New York,undefined
[4] NY 10027,undefined
[5] USA and Landau Institute for Theoretical Physics,undefined
[6] Kosygina str. 2,undefined
[7] 117940 Moscow,undefined
[8] Russia,undefined
[9] James Franck Institute of the University of Chicago,undefined
[10] 5640 S.Ellis Avenue,undefined
[11] Chicago,undefined
[12] IL 60637,undefined
[13] USA,undefined
[14] James Franck Institute and Enrico Fermi Institute of the University of Chicago,undefined
[15] 5640 S.Ellis Avenue,undefined
[16] Chicago,undefined
[17] IL 60637,undefined
[18] USA and Landau Institute for Theoretical Physics,undefined
[19] Joint Institute of Chemical Physics,undefined
[20] Kosygina str. 4,undefined
[21] 117334,undefined
[22] Moscow,undefined
[23] Russia and ITEP,undefined
[24] 117259,undefined
[25] Moscow,undefined
[26] Russia,undefined
来源：
Communications in Mathematical Physics | 1997年 / 188卷
关键词：
Difference Equation; Open Boundary; Time Equation; Standard Object; Discrete Classical;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The standard objects of quantum integrable systems are identified with elements of classical nonlinear integrable difference equations. The functional relation for commuting quantum transfer matrices of quantum integrable models is shown to coincide with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice with open boundaries. Elliptic solutions of Hirota's equation give a complete set of eigenvalues of the quantum transfer matrices. Eigenvalues of Baxter's Q-operator are solutions to the auxiliary linear problems for classical Hirota's equation. The elliptic solutions relevant to the Bethe ansatz are studied. The nested Bethe ansatz equations for Ak-1-type models appear as discrete time equations of motions for zeros of classical τ-functions and Baker-Akhiezer functions. Determinant representations of the general solution to bilinear discrete Hirota's equation are analysed and a new determinant formula for eigenvalues of the quantum transfer matrices is obtained. Difference equations for eigenvalues of the Q-operators which generalize Baxter's three-term T−Q-relation are derived.
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页码：267 / 304
页数：37
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