  In the numerical analysis of strongly correlated quantum lattice models one
of the leading algorithms developed to balance the size of the effective
Hilbert space and the accuracy of the simulation is the density matrix
renormalization group (DMRG) algorithm, in which the run-time is dominated by
the iterative diagonalization of the Hamilton operator. As the most
time-dominant step of the diagonalization can be expressed as a list of dense
matrix operations, the DMRG is an appealing candidate to fully utilize the
computing power residing in novel kilo-processor architectures. In the paper a
smart hybrid CPU-GPU implementation is presented, which exploits the power of
both CPU and GPU and tolerates problems exceeding the GPU memory size.
Furthermore, a new CUDA kernel has been designed for asymmetric matrix-vector
multiplication to accelerate the rest of the diagonalization. Besides the
evaluation of the GPU implementation, the practical limits of an FPGA
implementation are also discussed.
