FOR 1807:  Advanced Computational Methods for Strongly Correlated Quantum Systems

• Subject Area: Physics
• Term: from 2013 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 207383564

Strong correlation effects in quantum many-particle systems have become increasingly important for a number of phenomena in domains, which include material physics, nanostructures and cold atoms in optical lattices. Significant advances in numerical methods have made it possible to treat models of these physically interesting and potentially technologically important systems theoretically without approximations. These methods include quantum Monte Carlo, the density-matrix renormalisation group and its generalisations and self-consistent dynamical cluster methods. The aim of this Research Unit is to form a coherent network of active researchers in Germany, Austria and Switzerland, who have made significant contributions to this progress in numerical methods, in order to share expertise and ideas as well as to develop efficient algorithms for the current generation of high-performance computing hardware. There is potential to make significant advances in long-standing fundamental problems in correlated quantum systems such as frustrated magnetism, doped Mott insulators and interacting bosonic and coupled fermion-boson systems.

• DFG Programme: Research Units
• International Connection: Austria, Switzerland, United Kingdom

Projects

• Action-based quantum Monte Carlo approach to fermion-boson lattice models (Applicant Assaad, Fakher Fakhry )
• Action-based quantum Monte Carlo approach to fermion-boson lattice models (Applicant Hohenadler, Martin )
• Action-based quantum Monte Carlo approach to fermion-boson lattice models (Applicant Hohenadler, Martin )
• Advanced wave-function based methods for electron-phonon coupled systems (Applicants Heidrich-Meisner, Fabian ;  Jeckelmann, Eric )
• Cluster methods for spin systems (Applicant Manmana, Salvatore R. )
• Coordination Funds (Applicant Assaad, Fakher Fakhry )
• Density Matrix Renormalization Group in Hybrid Momentum Space (Applicant Noack, Reinhard M. )
• Efficient time evolution of quantum many-body systems in 2D with matrix product states (Applicant Pollmann, Frank )
• Entanglement entropies and spectra of interacting fermions from quantum Monte Carlo simulations (Applicant Assaad, Fakher Fakhry )
• Exact diagonalization at the petaflop scale (Applicant Läuchli, Andreas M. )
• Finite-Temperature Dynamics with Matrix Product State and Cluster Approaches (Applicants Daghofer, Maria ;  Manmana, Salvatore R. ;  Pruschke, Thomas )
• Matrix-product-state-based quantum impurity solvers (Applicant Schollwöck, Ulrich )
• Spin Dynamics of Exotic Quantum Magnets (Applicant Wessel, Ph.D., Stefan )
• Tensor network algorithms for two-dimensional strongly correlated lattice systems (Applicant Troyer, Matthias )
• Ultracold bosonic gases coupled to an optical cavity mode (Applicant Kollath, Corinna )

• Spokesperson: Professor Dr. Fakher Fakhry Assaad
• Deputy: Professor Dr. Reinhard M. Noack