Imaginary time propagation code for large-scale two-dimensional eigenvalue problems in magnetic fields

• Published in: Computer physics communications Vol. 184; no. 3; pp. 769 - 776
• Main Authors: Luukko, P.J.J., Räsänen, E.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2013
• Subjects: Diffusion algorithm; Eigenvalues; Factorization; Imaginary time propagation; Magnetic fields; Mathematical analysis; Mathematical models; Operators; Quantum chaos; Routines; Schroedinger equation; Schrödinger equation; Summaries; Two dimensional; Diffusion algorithm; Imaginary time propagation; Quantum chaos; Schrödinger equation
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2012.09.029

We present a code for solving the single-particle, time-independent Schrödinger equation in two dimensions. Our program utilizes the imaginary time propagation (ITP) algorithm, and it includes the most recent developments in the ITP method: the arbitrary order operator factorization and the exact inclusion of a (possibly very strong) magnetic field. Our program is able to solve thousands of eigenstates of a two-dimensional quantum system in reasonable time with commonly available hardware. The main motivation behind our work is to allow the study of highly excited states and energy spectra of two-dimensional quantum dots and billiard systems with a single versatile code, e.g., in quantum chaos research. In our implementation we emphasize a modern and easily extensible design, simple and user-friendly interfaces, and an open-source development philosophy. Program title: itp2d Catalogue identifier: AENR_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AENR_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 11310 No. of bytes in distributed program, including test data, etc.: 97720 Distribution format: tar.gz Programming language: C++ and Python. Computer: Tested on x86 and x86-64 architectures. Operating system: Tested under Linux with the g++ compiler. Any POSIX-compliant OS with a C++ compiler and the required external routines should suffice. Has the code been vectorised or parallelized?: Yes, with OpenMP. RAM: 1 MB or more, depending on system size. Classification: 7.3. External routines: FFTW3 (http://www.fftw.org), CBLAS (http://netlib.org/blas), LAPACK (http://www.netlib.org/lapack), HDF5 (http://www.hdfgroup.org/HDF5), OpenMP (http://openmp.org), TCLAP (http://tclap.sourceforge.net), Python (http://python.org), Google Test (http://code.google.com/p/googletest/) Nature of problem: Numerical calculation of the lowest energy solutions (up to a few thousand, depending on available memory), of a single-particle, time-independent Schrdinger equation in two dimensions with or without a homogeneous magnetic field. Solution method: Imaginary time propagation (also known as the diffusion algorithm), with arbitrary even order factorization of the imaginary time evolution operator Additional comments: Please see the README file distributed with the program for more information. The source code of our program is also available at https: //bitbucket.org/luukko/itp2d. Running time: Seconds to hours