Journal article

Bethe ansatz and ordinary differential equation correspondence for degenerate Gaudin models

  • Araby, Omar El Physics Department, University of Fribourg, Switzerland
  • Gritsev, Vladimir Physics Department, University of Fribourg, Switzerland
  • Faribault, Alexandre Institute for Theory of Statistical Physics, RWTH Aachen, Germany - Physics Department, ASC and CeNS, Ludwig-Maximilians-Universität, München, Germany
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  • Physical Review B - Condensed matter and materials physics. - 2012, vol. 85, no. 11, p. 115130
English In this work, we generalize the numerical approach to Gaudin models developed earlier by us [ Faribault, El Araby, Sträter and Gritsev Phys. Rev. B 83 235124 (2011)] to degenerate systems, showing that their treatment is surprisingly convenient from a numerical point of view. In fact, high degeneracies not only reduce the number of relevant states in the Hilbert space by a non-negligible fraction, they also allow us to write the relevant equations in the form of sparse matrix equations. Moreover, we introduce an inversion method based on a basis of barycentric polynomials that leads to a more stable and efficient root extraction, which most importantly avoids the necessity of working with arbitrary precision. As an example, we show the results of our procedure applied to the Richardson model on a square lattice.
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