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Exact diagonalization is a well-established method for simulating smallquantum systems. Its applicability is limited by the exponential growth of theso-called Hamiltonian matrix that needs to be diagonalized. Physical symmetriesare usually utilized to reduce the matrix dimension, and distributed-memoryparallelism is employed to explore larger systems. This paper focuses on theimplementation the core distributed algorithms, with a special emphasis on thematrix-vector product operation. Instead of the conventional MPI+X paradigm,Chapel is chosen as the language for these distributed algorithms.  We provide a comprehensive description of the algorithms and presentperformance and scalability tests. Our implementation outperforms thestate-of-the-art MPI-based solution by a factor of 7--8 on 32 compute nodes or4096 cores and exhibits very good scaling on up to 256 nodes or 32768 cores.The implementation has 3 times fewer software lines of code than the currentstate of the art while remaining fully generic.

Implementing scalable matrix-vector products for the exact diagonalization methods in quantum many-body physics