Sparse Modeling Approach for Quasiclassical Theory of Superconductivity

Abstract

We propose the sparse modeling approach for quasiclassical theory of superconductivity, which reduces the computational cost of solving the gap equations. The recently proposed sparse modeling approach is a consequence of the Green’s function having less information than its spectral function and hence is compressible without loss of relevant information. Using the intermediate representation of the Green’s function in the sparse modeling approach, the gap equation can be solved with only 10–100 sampled Matsubara Green’s functions, whereas the conventional quasiclassical theory requires 100–1000. The efficiency of the proposed method is demonstrated in bulk and vortex states, through self-consistently solve of the Eilenberger and gap equations. Consequently, the sparse modeling approach is concluded to be appropriate for all theoretical methods based on the Matsubara formalism in the quasiclassical theory of superconductivity.