The density matrix renormalization group for strongly correlated electron systems: A generic implementation

The purpose of this paper is (i) to present a generic and fully functional implementation of the density-matrix renormalization group (DMRG) algorithm, and (ii) to describe how to write additional strongly-correlated electron models and geometries by using templated classes. Besides considering general models and geometries, the code implements Hamiltonian symmetries in a generic way and parallelization over symmetry-related matrix blocks. Program summary: Program title: DMRG++. Catalogue identifier: AEDJ_v1_0. Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEDJ_v1_0.html. Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. Licensing provisions: See file LICENSE. No. of lines in distributed program, including test data, etc.: 15 795. No. of bytes in distributed program, including test data, etc.: 83 454. Distribution format: tar.gz. Programming language: C++, MPI. Computer: PC, HP cluster. Operating system: Any, tested on Linux. Has the code been vectorized or parallelized?: Yes. RAM: 1 GB (256 MB is enough to run included test). Classification: 23. External routines: BLAS and LAPACK. Nature of problem: Strongly correlated electrons systems, display a broad range of important phenomena, and their study is a major area of research in condensed matter physics. In this context, model Hamiltonians are used to simulate the relevant interactions of a given compound, and the relevant degrees of freedom. These studies rely on the use of tight-binding lattice models that consider electron localization, where states on one site can be labeled by spin and orbital degrees of freedom. The calculation of properties from these Hamiltonians is a computational intensive problem, since the Hilbert space over which these Hamiltonians act grows exponentially with the number of sites on the lattice. Solution method: The DMRG is a numerical variational technique to study quantum many body Hamiltonians. For one-dimensional and quasi one-dimensional systems, the DMRG is able to truncate, with bounded errors and in a general and efficient way, the underlying Hilbert space to a constant size, making the problem tractable. Running time: The test program runs in 15 seconds.