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

2013/10/31 by A. Zabrodin, Anton Zabrodin
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Bilinear interpolation #Black Holes and Theoretical Physics #Boundary value problem #Chain (unit) #Connection (principal bundle) #Eigenvalues and eigenvectors #Hierarchy #Master equation #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Operator (biology) #Physics #Pure mathematics #Quantum #Quantum mechanics #Spin (aerodynamics) #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.3842/sigma.2014.006

published as SIGMA 10 (2014), 006, 18 pages · arXiv admin note: text overlap with arXiv:1306.1111

arxiv created 2014/01/11 · openalex publication_date 2014/01/11 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Classical tau-function for quantum spin chains
• Solitons and Infinite Dimensional Lie Algebras
• FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS I: FUNCTIONAL RELATIONS AND REPRESENTATION THEORY
• The master T-operator for the Gaudin model and the KP hierarchy
• Bethe ansatz and Hirota equation in integrable models
• Spaces of quasi-exponentials and representations of the Yangian Y(gl_N)