2012/01/31 by Omar El Araby, Vladimir Gritsev, Alexandre Faribault · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Ansatz #Applied mathematics #Barycentric coordinate system #Bethe ansatz #Degenerate energy levels #Differential equation #Hilbert space #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Ordinary differential equation #Physics #Pure mathematics #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum mechanics #cond-mat.mes-hall #cond-mat.supr-con #quant-ph
paper · pdf · doi:10.1103/physrevb.85.115130
published as Phys. Rev. B 85, 115130 (2012) · 10 pages, 3 figures, published version
openalex publication_date 2012/03/29 · arxiv created 2012/04/25 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this work, we generalize the numerical approach to Gaudin models developed earlier by us [Faribault, El Araby, Str"ater, 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.