Journal Article

FZJ-2018-06303

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice

Krieg, S. (Corresponding author)FZJ* ; Luu, T.FZJ* ; Ostmeyer, J. ; Papaphilippou, P. ; Urbach, C.

2019
North Holland Publ. Co. Amsterdam

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Please use a persistent id in citations: http://hdl.handle.net/2128/21487  doi:10.1016/j.cpc.2018.10.008

Abstract: We present different methods to increase the performance of Hybrid Monte Carlo simulations of the Hubbard model in two-dimensions. Our simulations concentrate on a hexagonal lattice, though can be easily generalized to other lattices. It is found that best results can be achieved using a flexible GMRES solver for matrix inversions and the second order Omelyan integrator with Hasenbusch acceleration on different time scales for molecular dynamics. We demonstrate how an arbitrary number of Hasenbusch mass terms can be included into this geometry and find that the optimal speed depends weakly on the choice of the number of Hasenbusch masses and their values. As such, the tuning of these masses is amenable to automization and we present an algorithm for this tuning that is based on the knowledge of the dependence of solver time and forces on the Hasenbusch masses. We benchmark our algorithms to systems where direct numerical diagonalization is feasible and find excellent agreement. We also simulate systems with hexagonal lattice dimensions up to 102 × 102 and Nt=64 . We find that the Hasenbusch algorithm leads to a speed up of more than an order of magnitude.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)
2. Theorie der Starken Wechselwirkung (IAS-4)

Research Program(s):

1. 511 - Computational Science and Mathematical Methods (POF3-511) (POF3-511)
2. DFG project 35592816 - TRR 55: Hadronenphysik mit Gitter-QCD (35592816) (35592816)
3. DEEP-EST - DEEP - Extreme Scale Technologies (754304) (754304)
4. DEEP-ER - DEEP Extended Reach (610476) (610476)
5. DEEP - Dynamical Exascale Entry Platform (287530) (287530)
6. PRACE-5IP - PRACE 5th Implementation Phase Project (730913) (730913)

Appears in the scientific report 2019

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Database coverage:
; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; IF < 5 ; JCR ; NCBI Molecular Biology Database ; Nationallizenz ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Web of Science Core Collection

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