Overview

EDLib is a C++ template finite temperature Exact diagonalization solver for quantum electron models. The central class of the library is Hamiltonian<Storage, Model>, that is parametrized by Storage and Model:

• There exists a following set of implementation of models for common purposes:
  • HubbardModel<precision>. The finite Hubbard model cluster.
  • SingleImpurityAndersonModel<precision>. The single multi-orbital impurity Anderson Model.
• For the Hamiltonian matrix storage there are three implementation of sparse matrix storages:
  • SpinResolvedStorage<Model>. A storage that takes into account the case when hopping Hamiltonian can be expressed as Kronecker sum for each spin. This storage is implemented with MPI support.
  • SOCRSStorage<Model>. A storage that store only fermion signs for each element in Hamiltonian. This storage is implemented with OpenMP support.
  • CRSStorage<Model>. A simple CRS storage.

The resluting eigenpairs are stored as a set of EigenPair<precision, SymmetrySectorType> structures in the Hamiltonian object.

The following observable can be computed by means of Lanczos continuous fraction (Lanczos<Hamiltonian, Mesh, MeshArguments...> class template) of the Lehmann representation:

• Single-particle Green’s function (GreensFunction<Hamiltonian, Mesh, MeshArguments...> class template).
• Spin suseptibility (ChiLoc<Hamiltonian, Mash, MeshArguments...> class template). Greens functions are implemented on top of ALPSCore Greens functions module and can use either positive Matsubara frequency mesh or Real frequency mesh.

Look for examples in the “examples/” directory for a detailed information.

Installation

The code is is provided as a header-only library with a set of examples and tests. At least the edlib/Hamiltonian.h should be included in any derivative projects.

The eigensolver uses cpp-arnoldi, a header-only C++17 port of the ARPACK symmetric driver. Clone it alongside EDLib or point CMake at its location:

git clone https://github.com/Q-solvers/cpp-arnoldi ../cpp-arnoldi-main

To compile examples and tests create a build directory and run

1. cmake -DExamples=ON -DTesting=ON {path_to_edlib}
2. make
3. make test (for running tests)
4. example will be build in examples subdirectory

To build with MPI support add -DUSE_MPI=ON CMake flag. MPI library should be installed and ALPSCore library should be compiled with MPI support. To build with a specific ALPSCore library -DALPSCore_DIR=<path to ALPSCore> CMake flag.

Dependencies

• c++17-compatible compiler (gcc >= 7, clang >= 5, icpc >= 19)
• ALPSCore library >= 0.5.6-alpha3
• cpp-arnoldi (header-only, bundled or cloned alongside EDLib)
• BLAS and LAPACK
• MPI standard >= 2.1 (optional)
• git to fetch the code
• cmake >= 3.8.2 to build tests and examples (optional)

Authors

• Sergei Iskakov, iskakoff[at]q-solvers.ru, 2016-now
• Michael Danilov, 2016-now

Distribution

Open-source under MIT License.