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 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

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

\u3cp\u3eWe 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 summary: 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\u3c/p\u3

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 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 summary: 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 approac

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 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

Many-body localization: an introduction and selected topics

What happens in an isolated quantum system when both disorder and interactions are present? Over the recent years, the picture of a non-thermalizing phase of matter, the many-localized phase, has emerged as a stable solution. We present a basic introduction to the topic of many-body localization, using the simple example of a quantum spin chain which allows us to illustrate several of the properties of this phase. We then briefly review the current experimental research efforts probing this physics. The largest part of this review is a selection of more specialized questions, some of which are currently under active investigation. We conclude by summarizing the connections between many-body localization and quantum simulations.Comment: Review article. 28 pages, 8 figures, Comptes Rendus Physique (2018