Noncompact Heisenberg spin magnets from high-energy QCD: III. Quasiclassical approach

Abstract

The exact solution of the noncompact SL(2,C) Heisenberg spin magnet reveals a hidden symmetry of the energy spectrum. To understand its origin, we solve the spectral problem for the model within quasiclassical approach. In this approach, the integrals of motion satisfy the Bohr-Sommerfeld quantization conditions imposed on the orbits of classical motion. In the representation of the separated coordinates, the latter wrap around a Riemann surface defined by the spectral curve of the model. A novel feature of the obtained quantization conditions is that they involve both the alpha- and beta-periods of the action differential on the Riemann surface, thus allowing us to find their solutions by exploring the full modular group of the spectral curve. We demonstrate that the quasiclassical energy spectrum is in a good agreement with the exact results.

42 pages, Latex style, 9 figures

References in corpus (6)

• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation
• Noncompact Heisenberg spin magnets from high-energy QCD: II. Quantization conditions and energy spectrum
• Solution of the multi-reggeon compound state problem in multi-colour QCD
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• Analytic continuation of Bethe energies and application to the thermodynamic limit of the $SL(2,\mathbb{C})$ non-compact spin chains
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