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 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.

sparse-ir: optimal compression and sparse sampling of many-body propagators

“…Precomputed IRs for different cutoffs Λ have been released previously as the irbasis library [14]. Using this library, IR and sparse sampling has been successfully employed in numerous physics and chemistry applications [15,16,17,18,19,20,21,22,23,24,25,26,27,28].…”

Low rank Green's function representations applied to dynamical mean-field theory

“…Fortran, Python, and Julia libraries are available for both the IR with sparse sampling [15] and the DLR [16]. Low rank Green's function representations have been used to solve self-consistent diagrammatic equations in a variety of applications, including the SYK model [14,16,17], the self-consistent finite temperature GW method [13,18], Eliashberg-type equations for superconductivity [19][20][21][22], and Bethe-Salpeter-type equations for Hubbard models [23].…”