KONWIHR

COMPETENCE NETWORK FOR TECHNICAL, SCIENTIFIC HIGH PERFORMANCE COMPUTING IN BAVARIA

HQS@HPC-II

Strongly correlated quantum systems on high performance computers

The challenge of understanding the complex physical properties of highly correlated quantum systems has stimulated intense work on generic microscopic model Hamiltonians. Topical issues are charge, spin, and heat transport, quantum phase transitions, particle real-time dynamics, quantum uctuation, temperature, detuning and decoherence effects, in particular in electronically low-dimensional materials or in geometrically restricted quantum systems/devices. The project addresses these problems by employing large-scale numerical investigations on high-end supercomputers. In particular we apply the density matrix renormalization group (DMRG) scheme in order to examine the intervening metallic phase at the spin-density-wave charge-density-wave transition in the one-dimensional Holstein-Hubbard model. Moreover we explore charge transport within a correlated/ uctuating background medium by means of an effective lattice model with a novel form of fermion-boson coupling. Combining exact diagonalisation, DMRG and kernel polynomial methods, we study the ground-state and spectral properties of this model, and discuss the possibility of a metal-insulator quantum phase transition in relation to Mott and Peierls transition scenarios. By means of recently developed Chebyshev expansion and Chebyshev space techniques we investigate the time evolution of finite quantum systems, and inspect the effects of the coupling of quantum systems to fermionic and bosonic baths.

As the predecessor KONWIHR project "HQS@HPC" has shown prominently, the importance of high-performance numerical software cannot be overrated even when using the most advanced algorithms. An explicit goal of this project is thus the further advancement of our high-performance implementations. The "hot spot" in our exact diagonalization codes is sparse matrix-vector multiplication (sMVM). We will employ recent developments in sMVM optimization to improve performance of ED. Furthermore, we will make use of data structures that enable architecture-specific data access optimizations. For shared-memory and hybrid ED codes, correct ccNUMA page placement will be paramount. As the rigid boundary conditions for ccNUMA placement work against optimal load balancing, the use of hybrid, hierarchical implementations that are ideally mapped to the core--socket--node--cluster structure of modern HPC systems will be thoroughly evaluated.