An eigenvalue problem related to the non-linear sigma-model: analytical and numerical results

Details An eigenvalue problem related to the non-linear sigma-model: analytical and numerical results An eigenvalue problem related to the non-linear sigma-model: analytical and numerical results

2003-07-06

arxiv.org/abs/math-ph/0307010v1

J.Phys.A36:11881-11900,2003

Physics

Mathematical Physics

18 pages, AmsLatex, Axodraw

Scientific paper

10.1088/0305-4470/36/47/014

An eigenvalue problem relevant for non-linear sigma model with singular metric is considered. We prove the existence of a non-degenerate pure point spectrum for all finite values of the size R of the system. In the infrared (IR) regime (large R) the eigenvalues admit a power series expansion around IR critical point R\to\infty. We compute high order coefficients and prove that the series converges for all finite values of R. In the ultraviolet (UV) limit the spectrum condenses into a continuum spectrum with a set of residual bound states. The spectrum agrees nicely with the central charge computed by the Thermodynamic Bethe Ansatz method

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