Sublattice Coding Algorithm and Distributed Memory Parallelization for Large-Scale Exact Diagonalizations of Quantum Many-Body Systems

Abstract

We present algorithmic improvements for fast and memory-efficient use of discrete spatial symmetries in Exact Diagonalization computations of quantum many-body systems. These techniques allow us to work flexibly in the reduced basis of symmetry-adapted wave functions. Moreover, a parallelization scheme for the Hamiltonian-vector multiplication in the Lanczos procedure for distributed memory machines avoiding load balancing problems is proposed. We demonstrate that using these methods low-energy properties of systems of up to 50 spin-1/2 particles can be successfully determined.

10 pages, 5 figures

References in corpus (4)

• Scalable multi-particle entanglement of trapped ions
• Fractional quantum Hall states at zero magnetic field
• Verification of quantum computation: An overview of existing approaches
• Divide and conquer the Hilbert space of translation-symmetric spin systems

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