Discrete Lehmann representation of imaginary time Green's functions

We present an efficient basis for imaginary time Green's functions based on a low-rank decomposition of the spectral Lehmann representation. The are simply set well-chosen exponentials, so corresponding expansion may be thought as discrete form representation using effective density which is sum $\ensuremath{\delta}$ functions. determined only by upper bound product $\ensuremath{\beta}{\ensuremath{\omega}}_{max}$, with $\ensuremath{\beta}$ inverse temperature and ${\ensuremath{\omega}}_{max}$ energy cutoff, user-defined error tolerance $\ensuremath{\epsilon}$. number $r$ scales $O(log(\ensuremath{\beta}{\ensuremath{\omega}}_{max})log(1/\ensuremath{\epsilon}))$. particular function can recovered interpolation at nodes. Both nodes obtained rapidly standard numerical linear algebra routines. Due to simple basis, explicitly transformed Matsubara frequency domain, or directly grid. benchmark efficiency cases, high-precision solution Sachdev-Ye-Kitaev equation low temperature. compare our approach related intermediate method, introduce improved algorithm build sampling