Andor Menczer (ELTE), Áron Vízkeleti (Wigner RCP), Mihály Máté (Wigner RCP) and Örs Legeza (Wigner RCP) - (2022.09.01 - 2022.11.30)

Abstract: Numerical simulation of quantum systems where strong interaction between atomic spins and itinerant electrons is present, and at the same time cannot be described with perturbative methods are in the focus of modern physics. These simulations are challenging because computational resources, in general, scale exponentially with system size. Developing algorithms to simulate these systems with polynomial complexity is one of the most heavily researched subjects today.

The density-matrix renormalization group (DMRG) algorithm is one such method, with the additional advantage that the underlying tensor algebra, in light of the conserved quantum numbers, can be broken up into millions of independent tasks. This makes this algorithm ideal for MPI and GPU based massive parallelization. Our research group have been researching the subject for two decades. A GPU based kernel application have been implemented recently thanks to Andor Menczer (ELTE graduate student). In this project we would like to test, and based on the results, optimize this application. At the same time, we would also like to apply it to two-dimensional electron systems, strongly correlated molecular clusters, and atomic nuclei.

The project involves Andor Menczer (ELTE), Áron Vízkeleti (WignerFK), Mihály Máté (WignerFK) and Örs Legeza (WignerFK). The source code was written in Matlab, and a standalone version was compiled using Matlab Compiler. We wish to carry out the testing, fine-tuning and application to large systems in steps. The GPU kernel was built using the Matlab Paralelization Toolbox, and CODA Coder. For the first step, we would like to ask for a three months long interval of access to one of the nodes (cluster 1, 2, 3, 4) that access NVIDIA graphics cards.

We plan to publish the simulation results in prestigious international journals, like the ones our previous work appeared in [1,2]

[1] The density matrix renormalization group algorithm on kilo-processor architectures: implementation and trade-offs, Csaba Nemes, Gergely Barcza, Zoltán Nagy, Örs Legeza, Péter Szolgay, Computer Physics Communications Volume 185, Issue 6, June 2014, Pages 1570-1581

[2] Massively parallel quantum chemical density matrix renormalization group method, Jiří Brabec, Jan Brandejs, Karol Kowalski, Sotiris Xantheas, Örs Legeza, Libor Veis, Computational Chemistry, https://doi.org/10.1002/jcc.26476