Sparse modeling approach for quasiclassical theory of superconductivity

TL;DR

This paper introduces a sparse modeling method that significantly reduces computational costs in solving quasiclassical superconductivity equations by leveraging the compressibility of Green's functions, enabling efficient calculations with fewer sampled functions.

Contribution

The paper presents a novel sparse modeling approach using intermediate representation to efficiently solve gap equations with fewer Green's function samples in superconductivity theory.

Findings

Reduces the number of Green's functions needed from 100-1000 to 10-100.

Demonstrates efficiency in bulk and vortex states calculations.

Applicable to all Matsubara formalism-based methods in quasiclassical 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 based on the fact that the Green's function has less information than its spectral function and hence is compressible without loss of relevant information. With the use of the so-called intermediate representation of the Green's function in the sparse modeling approach, one can solve the gap equation with only 10-100 sampled Matsubara Green's functions, while the conventional quasiclassical theory needs 100-1000 ones. We show the efficiency of our method in bulk and vortex states, by self-consistently solving the Eilenberger equations and gap equations. We claim that the sparse modeling approach is appropriate in all theoretical methods based on the Matsubara formalism in the quasiclassical theory of superconductivity.