1201.5542 (Omar El Araby et al.)

BA/ODE Correspondence for Degenerate Gaudin Models    [PDF]

Omar El Araby, Vladimir Gritsev, Alexandre Faribault

In this work, we generalize the numerical approach to Gaudin models developed
earlier by us 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 to write the relevant equations
in the form of sparse matrix equations. Moreover, we introduce a new inversion
method based on a basis of barycentric polynomials which 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.

View original: http://arxiv.org/abs/1201.5542