The Supercomputer MACH-2: Use Cases
[Back to Use Cases]
Use Case: Diagonalization of Very Large Sparse Matrices
Involved Scientists
- C. Ganahl (Institut für Theoretische Physik, Leopold-Franzens-Universität Innsbruck)
- C. Boos, M. Lajkó, P. Nataf, A. M. Läuchli, K. Penc, K. P. Schmidt, F. Mila
(Institute for Theoretical Physics, FAU Erlangen-Nürnberg,
Institute of Physics, Ecole Polytechnique Fédérale de Lausanne,
Laboratoire de Physique et Modélisation des Milieux Condensés, Université Grenoble
Alpes and CNRS, Institute for Solid State Physics and Optics, Wigner Research Centre for Physics,
Budapest)
Description of the Application
Quantum spin liquids (QSLs) are exotic phases of matter that have been
extensively studied in the last decades due to their interesting magnetic
properties and possible technological applications, e.g. in quantum
computers. The identification of QSLs is, however, a very challenging
problem since exact solutions for strongly correlated condensed matter
systems rarely exist. Numerical methods are often the only option left.
Figure: Ground-state energies as a function of the coupling constants and
phase borders of a SU(3) symmetric spin model on the triangular lattice.
(CC BY 4.0 attributed to [1])
We studied SU(N) symmetric spin systems on regular lattices. To obtain the
lowest lying energy eigenstates and eigenvalues we used an iterative
eigenvalue solver algorithm. The Hamiltonians for such systems are huge
sparse matrices. The size of this matrices as well as the method used
require a huge amount of memory. Furthermore, the structure of the problem
under investigation leads to massive communication between the threads,
which makes an implementation on a distributed memory system not feasible.
Using the Mach2 Supercomputer with its extensive amount of shared memory
allowed us to identify a QSL phase in a SU(3) symmetric spin model on the
triangular lattice.
References
- Boos, C., Ganahl, C. J., Lajkó, M., Nataf, P., Läuchli, A. M., Penc, K., ... & Mila, F. (2020). Time-reversal symmetry breaking Abelian chiral spin liquid in Mott phases of three-component fermions on the triangular lattice. Physical Review Research, 2(2), 023098.
DOI: 10.1103/PhysRevResearch.2.023098
JKU Scientific Computing Administration