Green's functions

Detailed Description

Generic containers for Green's functions, self energies and other important functions in quantum many-body physics.

The Green's functions in the TRIQS library are generic containers for functions which are not known analytically. As the name suggests, they are intended to be used for quantum many-body Green's functions, self energies or other correlation functions, but they can in principle be used for more general functions.

The central container is triqs::gfs::gf, a class template parameterised by two ingredients:

• a mesh (see Meshes) that fixes the mathematical domain of the function, how it is represented in memory and how it is evaluated, and
• a target, which fixes the value stored at each mesh point: a scalar (triqs::gfs::scalar_valued), a matrix (triqs::gfs::matrix_valued) or a higher-rank tensor (triqs::gfs::tensor_valued). The target types live in GF targets.

Each container comes with non-owning view classes, triqs::gfs::gf_view and triqs::gfs::gf_const_view, that refer to the data of an existing Green's function without copying it. The generic requirements shared by all of these types are spelled out as C++20 concepts in GF concepts.

Many physical problems are naturally block-diagonal (e.g. in spin or orbital sectors). triqs::gfs::block_gf and its view triqs::gfs::block_gf_view represent a vector of Green's functions sharing a common type, while triqs::gfs::block2_gf provides the two-index analogue.

Around these containers the module provides a library of physical operations such as density and high-frequency tail evaluation (GF functions), HDF5 serialisation (GF input/output), transforms between representations such as the Fourier transform and the Padé analytic continuation (GF transforms), and factory functions, expression templates and other utilities (GF utilities).

Topics
	GF concepts
	Concepts that specify the requirements for Green's function types.
	GF containers
	Green's function container and view types.
	GF functions
	Physical operations acting on Green's functions.
	GF input/output
	HDF5 serialisation of Green's functions.
	GF transforms
	Transforms between different Green's function representations.
	GF utilities
	Operations and utilities acting on Green's function containers.