Faculté des sciences

Bethe ansatz and ordinary differential equation correspondence for degenerate Gaudin models

Araby, Omar El ; Gritsev, Vladimir ; Faribault, Alexandre

In: Physical Review B - Condensed matter and materials physics, 2012, vol. 85, no. 11, p. 115130

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... Plus

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    Summary
    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.