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This work studies different alternatives for parallelization of ground-state DMRG, with a focus on shared memory multiprocessor systems. Exploiting the parallelism in the dominant part of a DMRG calculation (diagonalization of the superblock Hamiltonian), speedups of 5 to 6 on 8-CPU machines can be achieved. A performance analysis gives hints as to which machine is best siuted for the task. The parallelized DMRG code is then applied to current problems in theoretical solid state physics with electronics, bosonic and spin degrees of freedom. Stripe-like modulations of the hole density in the ground state of doped Hubbard with cylindrical boundary conditions are idenficied in the thermodynamic limit using extrapolation techniques. In the 1D Holstein model of spinless fermions at half filling, Luttinger parameters and the charge structure factor are determinde in order to derive the phase diagram that had previously been established only on small lattices. For the 1D half-filled Holstein-Hubbard model, a finite size analysisof spine and charge excitation gaps in the relevant sectors (Mott insulator, Peierls band insulator and bipolaronic Peierls insulator) is able to yield the phase diagram as well. Finally, is the Heisenberg spin chain with dynamical phonons is considered as a relevant model for a spin-Peierls transition in Copper Germanate. Using DMRG, the relation between singlet-triplet excitation gap and dynamical dimeriaztion is calculated for the first time.

We introduce PVSC-DTM (Parallel Vectorized Stencil Code for Dirac and Topological Materials), a library and code generator based on a domain-specific language tailored to implement the specific stencil-like algorithms that can describe Dirac and topological materials such as graphene and topological insulators in a matrix-free way. The generated hybrid-parallel (MPI+OpenMP) code is fully vectorized using Single Instruction Multiple Data (SIMD) extensions. It is significantly faster than matrix-based approaches on the node level and performs in accordance with the roofline model. We demonstrate the chip-level performance and distributed-memory scalability of basic building blocks such as sparse matrix-(multiple-) vector multiplication on modern multicore CPUs. As an application example, we use the PVSC-DTM scheme to (i) explore the scattering of a Dirac wave on an array of gate-defined quantum dots, to (ii) calculate a bunch of interior eigenvalues for strong topological insulators, and to (iii) discuss the photoemission spectra of a disordered Weyl semimetal.