The EDIpack2 Fortran Library

Here we give an overview of the structure of the EDIpack2 library, with a detailed description of the relevant modules and procedures.

Library Frontend 

The EDIPACK2 module represents the main user interface (or Fortran API) of the EDIpack2 library. This modules gives access to all the available procedures and variables as needed to solve quantum impurity problems.

Core Solver Routines 

The module ED_MAIN wraps the EDIpack2 algorithm into three functions, one for each step: initialization, solution and finalization.

General Environment

This part of the library includes a set of modules which contain variables or procedures serving the rest of the code. The set includes:

ED_INPUT_VARS which defines global input variables and input read method.

ED_VARS_GLOBAL containing global shared variables and classes,such as the key class effective_bath which gathers the different bath components according to value of bath_type and ed_mode.

ED_AUX_FUNX defining procedures which are used throughout the code.

ED_SETUP which handles global memory (de)allocation and the evaluation of the dimensions of the symmetry sectors.

ED_PARSE_UMATRIX which describes how a custom interaction Hamiltonian can be initialized.

Classes

This is a group of modules implementing different classes which are used throughout the software to deal with special needs. The group includes:

The ED_SPARSE_MATRIX class, which contains the implementation of a suitable Compact Row Stored (CRS) sparse matrix, used to store the sparse Hamiltonians in each symmetry sector.

The ED_EIGENSPACE class, which implements an ordered single linked list to efficiently store the lower part of the energy spectrum.

The ED_GFMATRIX class which stores the results of the dynamical Lanczos calculation of dynamical correlation functions in terms of weights and poles of the Kallen-Lehmann representation.

Symmetry Sectors 

The ED_SECTOR module implements the construction of the symmetry sectors for the three sets of quantum numbers \(\vec{Q}\) considered in EDIpack2, that we recall are:

\(\vec{Q}=[\vec{N}_\uparrow,\vec{N}_\downarrow]\) for which either the number of total or orbital spin up and down electrons is conserved: NORMAL
\(\vec{Q}=S_z\) with conserved total magnetization: SUPERConducting
\(\vec{Q}=N_{\rm tot}\) where spin degrees freedom is not fully conserved: NON-SU(2)

Quantum Impurity Bath 

In EDIpack2 the bath is handled using a Reverse Communication Strategy. All the procedures designed to define or handle the discretized bath as well as those to evaluate suitable functions of the bath are grouped in set of modules.

Hamiltonian 

This part of the EDIpack2 code implements the setup of the sector Hamiltonian in each operational modes, corresponding to the choice of one of the symmetries implemented in the code selected by the variable ed_mode = normal, superc, nosu2. See ED_SECTOR for more info about the symmetries implemented in the code.

Any of three different mode is implemented in a distinct class of modules performing all the operations required for the construction of the Hamiltonian and the definition of the corresponding matrix vector product, required by the Arpack/Lanczos.

Exact Diagonalization 

This part of the EDIpack2 code implements the exact diagonalization of the general, single-site, multi-orbital quantum impurity problem in each of the specific symmetry implemented in the code. The operational modes are selected by the variable ed_mode = normal, superc, nosu2 (see ED_SECTOR for more info about the symmetries implemented in the code).

As above, we implemented the three different channels in distinct class of modules.

Green's Functions 

This part of the EDIpack2 code implements the calculation of the impurity interacting Green's functions, self-energy functions and impurity susceptibilities. Calculations are performed in each operational mode, corresponding to the choice of the specific symmetry implemented in the code, i.e. which quantum numbers are to be conserved. The operational modes are selected by the variable ed_mode = normal, superc, nosu2 (see ED_SECTOR for more info about the symmetries implemented in the code).

Susceptibilities 

This part of the EDIpack2 code implements the calculation of the impurity susceptibilities in different physical channels: spin, charge, pair and excitonic. The calculations are performed for ed_mode = normal.

Observables 

This part of the EDIpack2 code implements the calculation of the impurity observables and static correlations, such as density, internal energy or double occupation. Calculations are performed in each operational mode, corresponding to the choice of the specific symmetry implemented in the code, i.e. which quantum numbers are to be conserved. The operational modes are selected by the variable ed_mode = normal, superc, nosu2. The observables are printed in plain text files and are accessible to the user through the routines lited in ED_IO (see ED_SECTOR for more info about the symmetries implemented in the code).

Reduced Density Matrix 

This part of the EDIpack2 code implements the calculation of the impurity Reduced Density Matrix (RDM). Calculations are performed in each operational mode, corresponding to the choice of the specific symmetry implemented in the code, i.e. which quantum numbers are to be conserved. The operational modes are selected by the variable ed_mode = normal, superc, nosu2. The evaluation of the RDM exploit an efficient sparse algorithm to avoid tracing over the exponentially many bath configuration. The RDM is saved to file and made available to the user through the routines listed in ED_IO.

Input/Output 

This module provides access to the results of the exact diagonalization. All quantities such as dynamical response functions, self-energy components or impurity observables can be retrieved using specific functions. Additionally we provide procedure to perform on-the-fly re-calculation of the impurity Green's functions and self-energy on a given arbitrary set of points in the complex frequency domain.

Bath Optimization 

In this module we provide to the user a generic function ed_chi2_fitgf() performing the minimization of a user provided Weiss field against the corresponding model of non-interacting Anderson Green's function with the aim of updating the user bath parameters.