Implementation of the Lanczos algorithm for the Hubbard model on the Connection Machine system
- Supercomputer Computations Research Institute, Florida State University, B-186, Tallahassee, Florida 32306-4052 (United States)
- Thinking Machines Corporation, Cambridge, Massachusetts 02142-1264 (United States)
An implementation of the Lanczos algorithm for the exact diagonalization of the two dimensional Hubbard model on a 4[times]4 square lattice on the Connection Machine CM-2 system is described. The CM-2 is a massively parallel machine with distributed memory. The program is written in C/PARIS. This implementation minimizes memory usage by generating the matrix elements as needed instead of storing them. The Lanczos vectors are stored across the local memory of the processors. Using translational symmetry only, the dimension of the Hilbert space at half filling is more than 10 million. A speed of about 2.4 min per iteration is achieved on a 64K CM-2. This implementation is scalable. Running it on a bigger machine with more processors speeds up the process. The performance analysis of this implementation is shown and discuss its advantages and disadvantages are discussed.
- DOE Contract Number:
- FC05-85ER25000
- OSTI ID:
- 6937379
- Journal Information:
- Computers in Physics; (United States), Vol. 6:6; ISSN 0894-1866
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
HAMILTONIANS
COMPUTER CALCULATIONS
ALGORITHMS
HILBERT SPACE
MATRIX ELEMENTS
MEMORY MANAGEMENT
PARALLEL PROCESSING
SUPERCOMPUTERS
BANACH SPACE
COMPUTERS
DIGITAL COMPUTERS
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
PROGRAMMING
QUANTUM OPERATORS
SPACE
661300* - Other Aspects of Physical Science- (1992-)