Efficient imaginary time calculations using the discrete Lehmann representation

The discrete Lehmann representation (DLR) is a simple, generic, and highly efficient method of approximating single-particle Green's functions, and related quantities, in imaginary time and frequency. It is therefore a useful basic tool in a variety of algorithms for quantum many-body physics calculations. The DLR is built from an explicit basis of exponentials, enabling the straightforward execution of standard operations, and the number of basis functions scales only logarithmically with the product of the inverse temperature and spectral width. I will describe a few recent applications, including the efficient evaluation of imaginary time diagrams, a simple solution of the "tail-fitting" problem in the dynamical mean-field theory loop, and the discretization of imaginary time degrees of freedom on the Keldysh contour. I will also mention a stand-alone C++ implementation, cppdlr, as well as the implementation of the DLR in the TRIQS library.