Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 006, 18 pages      arXiv:1310.6988      https://doi.org/10.3842/SIGMA.2014.006
Contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa

The Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy

Anton Zabrodin a, b, c, d
a) Institute of Biochemical Physics, 4 Kosygina, 119334, Moscow, Russia
b) ITEP, 25 B. Cheremushkinskaya, 117218, Moscow, Russia
c) National Research University Higher School of Economics, 20 Myasnitskaya Ulitsa, Moscow 101000, Russia
d) MIPT, Institutskii per. 9, 141700, Dolgoprudny, Moscow region, Russia

Received October 18, 2013, in final form January 08, 2014; Published online January 11, 2014

Abstract
Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we show how to construct the master $T$-operator for the quantum inhomogeneous ${\rm GL}(N)$ $XXX$ spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspond to eigenvalues of the master $T$-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum spin chain and the classical Ruijsenaars-Schneider system of particles.

Key words: quantum integrable spin chains; classical many-body systems; quantum-classical correspondence; master $T$-operator; tau-function.

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