Diagonalisation of quantum observables on regular lattices and general graphs

Abstract

In the study of quantum mechanical systems, exact diagonalisation (ED) methods play an extremely important role. We have developed an ED code named DoQO (Diagonalisation of Quantum Observables). This code is capable of constructing and diagonalising the observables for spin 1 2 and spinless fermionic particles with many body interactions on arbitrary graphs using massively parallel distributed memory machines. At the same time, the code can exploit physical symmetries to reduce the size of the relevant basis set and provide useful physical information about each eigenstate. DoQO has been employed successfully to directly diagonalise systems with basis sets containing a billion elements. By exploiting symmetries it has been possible to perform calculations on systems with 36 spin 1 2 particles. Here we present essential background details, the structure and usage of DoQO, and a study of the performance characteristics of DoQO on different machines. Program summary Program title: DoQO Catalogue identifier: AEII_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEII_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 81 845 No. of bytes in distributed program, including test data, etc.: 495 379 Distribution format: tar.gz Programming language: C++ (dependencies require Fortran) Computer: Standard workstations and distributed memory machines Operating system: Any operating system with C++, Fortran, MPI, PETSc and SLEPc (code developed and tested on OS X and Linux) Has the code been vectorised or parallelised?: Yes code uses MPI for interprocess communication. One to thousands of processors may be used RAM: Depends on problem size. Ranges from MBs to TBs Classification: 7.8 External routines: PETSc, SLEPc, LAPACK, BLAS, MPI, BOOST, tinyxml Nature of problem: To calculate the low lying eigenvalues and eigenstates of quantum observables for spin 1 2 and spinless fermionic systems on arbitrary graphs efficiently in parallel. Solution method: Large scale linear scaling iterative exact diagonalisation methods are used on distributed memory machines. Physical symmetries are exploited to extend the size of systems which can be treated and to provide important additional information about the eigenstates. Restrictions: The size of the systems that DoQO can handle is restricted by the amount of available memory. Unusual features: The main feature that makes DoQO stand out from other diagonalisation codes is its ability to exploit physical symmetries efficiently using parallel computer architectures without the use of model specific optimisations. The ability to treat systems with arbitrarily complex interactions is also unique. Running time: The running time ranges from seconds to hours depending on the problem size and computational resources used.