Massively parallel implementation and approaches to simulate quantum dynamics using Krylov subspace techniques

We have developed an application and implemented parallel algorithms in order to provide a computational framework suitable for massively parallel supercomputers to study the unitary dynamics of quantum systems. We use renowned parallel libraries such as PETSc/SLEPc combined with high-performance co...

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Bibliographic Details
Published in:Computer physics communications 2019-02, Vol.235, p.477-488
Main Authors: Brenes, Marlon, Varma, Vipin Kerala, Scardicchio, Antonello, Girotto, Ivan
Format: Article
Language:English
Subjects:
Distributed memory parallelism
Krylov subspace methods
Strongly interacting systems
Unitary quantum dynamics
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Summary:We have developed an application and implemented parallel algorithms in order to provide a computational framework suitable for massively parallel supercomputers to study the unitary dynamics of quantum systems. We use renowned parallel libraries such as PETSc/SLEPc combined with high-performance computing approaches in order to overcome the large memory requirements to be able to study systems whose Hilbert space dimension comprises over 9 billion independent quantum states. Moreover, we provide descriptions of the parallel approach used for the three most important stages of the simulation: handling the Hilbert subspace basis, constructing a matrix representation for a generic Hamiltonian operator and the time evolution of the system by means of the Krylov subspace methods. We employ our setup to study the evolution of quasidisordered and clean many-body systems, focussing on the return probability and related dynamical exponents: the large system sizes accessible provide novel insights into their thermalization properties. Program Title: DSQMKryST Program Files doi:http://dx.doi.org/10.17632/f6vty3wkwj.1 Licensing provisions: BSD 3-clause Programming language: C++ Supplementary material:https://github.com/mbrenesn/DSQMKryST External routines/libraries: PETSc (https://www.mcs.anl.gov/petsc/), SLEPc (http://slepc.upv.es), Boost C++ (http://www.boost.org) Nature of problem: Unitary dynamics of quantum mechanical many-body systems Solution method: Krylov subspace techniques (Arnoldi procedure) with a massively parallel, distributed memory approach
ISSN:0010-4655
1879-2944
DOI:10.1016/j.cpc.2018.08.010