HQS@HPC-II: Strongly correlated quantum systems on high performance computers

Project summary

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 fluctuation, 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/ fluctuating 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.

KONWIHR funding and follow-up projects

  • HQS@HPC2 is a follow-up project of HQS@HPC
  • KONWIHR funding of HQS@HPC2: 9/2008 - 8/2011


  • Dr. Georg Hager, Regionales Rechenzentrum Erlangen, Uni-Erlangen
  • Prof. Dr. Holger Fehske, Institut für Physik, Universität Greifswald

Project staff:

  • Dr. Gerald Schubert, Regionales Rechenzentrum Erlangen, Uni-Erlangen

Publications and presentations

  • A. Alvermann, H. Fehske: Non-equilibrium current and electron pumping in nanostructures, J. Phys. Conf. Ser., 200 (2010) 012005.
  • S. Ejima, H. Fehske: DMRG analysis of the SDW-CDW crossover region in the 1D half-filled Hubbard-Holstein model, J. Phys. Conf. Ser., 200 (2010) 012031.
  • H. Fehske, G. Hager: Luttinger, Peierls of Mott? Quantum Phase Transitions in Strongly Correlated 1D Electron-Phonon Systems, "Metal-to-Nonmetal Transitions" -- Springer Series in Material Sciences (Ed: F. Hensel, P. Edwards, R. Redmer), Springer (Berlin, Heidelberg), 132 (2010) 1-22.
  • J. Schleede, G. Schubert, H. Fehske: Comment on "Anderson transition in disordered graphene", Europhys. Lett., 99 (2010) 17002.
  • G. Schubert, J. Schleede, K. Byczuk, H. Fehske, D. Vollhardt: Distribution of the local density of states as a criterion for Anderson localization: Application to various lattices in two and three dimensions, Phys. Rev. B, 81 (2010) 155106.
  • S. Ejima, G. Hager, H. Fehske: Quantum phase transitions in a 1D transport model with boson affected hopping: Luttinger liquid versus charge-density-wave behavior, Phys. Rev. Lett., 102 (2009) 106404.
  • S. Ejima, H. Fehske: One-Dimensional Quantum Transport Affected by a Background Medium: Fluctuations versus Correlations, Phys. Rev. B, 80 (2009) 155101.
  • S. Ejima, H. Fehske: Luttinger parameters and momentum distribution function for the half-filled spinless fermion Holstein model: A DMRG approach, Europhys. Lett., 89 (2009) 27001.
  • H. Fehske, J. Schleede, G. Schubert, G. Wellein, V.S. Filinov, A.R. Bishop: Numerical approaches to time evolution of complex quantum systems, Phys. Lett. A, 373 (2009) 2182.
  • G. Schubert, J. Schleede, H. Fehske: Anderson disorder in graphene nanoribbons: A local distribution approach, Phys. Rev. B, 79 (2009) 235116.
  • G. Schubert, V.S. Filinov, K. Matyash, R. Schneider, H. Fehske: Comparative study of semiclassical approaches to quantum dynamics, Int. J. Mod. Phys. C, 20 (2009) 1155.
  • H. Fehske, G. Hager, E. Jeckelmann: Metallicity in the half-filled Holstein-Hubbard model, Europhys. Lett., 84 (2008) 57001. External link: DOI: 10.1209/0295-5075/84/57001
  • V.S. Filinov, G. Schubert, P. Levashov, M. Bonitz, H. Fehske, V.E. Fortov, A.V. Filinov: Center-of-mass tomographic approach to quantum dynamics, Phys. Lett. A, 372 (2008) 5064.
  • G. Schubert, H. Fehske: Diffusion and localization in quantum random resistor networks, Phys. Rev. B, 78 (2008) 155115. External link: DOI: 10.1103/PhysRevB.78.155115
  • G. Wellein, H. Fehske, A. Alvermann, D. M. Edwards: Quantum phase transition in a two-channel transport model, Phys. Rev. Lett., 101 (2008) 136402. External link: DOI: 10.1103/PhysRevLett.101.136402
  • See HQS@HPC for further publications and presentations related to the project and its forerunner