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

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 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.

arXiv admin note: text overlap with arXiv:1306.1111

References in corpus (10)

• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• On Three Dimensional Quiver Gauge Theories and Integrability
• From Characters to Quantum (Super)Spin Chains via Fusion
• Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
• Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz
• The master T-operator for the Gaudin model and the KP hierarchy
• Gaudin Hamiltonians generate the Bethe algebra of a tensor power of vector representation of gl_N
• Rational Ruijsenaars-Schneider hierarchy and bispectral difference operators
• Bethe ansatz and Hirota equation in integrable models
• Spaces of quasi-exponentials and representations of the Yangian Y(gl_N)

Cited by in corpus (6)

• Relativistic Classical Integrable Tops and Quantum R-matrices
• Off-shell scalar products for the $XXZ$ spin chain with open boundaries
• Quantum spin chains and integrable many-body systems of classical mechanics
• Toda lattice hierarchy and trigonometric Ruijsenaars-Schneider hierarchy
• Elliptic solutions to Toda lattice hierarchy and elliptic Ruijsenaars-Schneider model
• Incarnations of XXX $\widehat{{\mathfrak{sl}}_N}$ Bethe ansatz equations and integrable hierarchies