Implementation of explicit SU(2)-invariance in tensor product states and applications to renormalization group calculations

• Applicant: Professor Dr. Andreas Kluemper
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2008 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 91564163

The project is devoted to modern renormalization group treatments of quantum information theory and their application to correlated electronic systems as well as their further development. Tensor product states will be used for the investigation of quantum spin systems in one and two spatial dimensions with a consequent local implementation of the non-Abelian su(2)-invariance. This implementation will drastically facilitate the search of the energy minimum as the local factors of the tensor product states are parameterized by rather few correlation coefficients. In this way, for one spatial dimension the thermodynamical limit is directly accessible. In two spatial dimensions a recursive treatment combined with a truncation of the local auxiliary states will be employed. The main goalsof the project are the calculation of the auto-correlation function of the spin-1/2 Heisenbergchain and the ground-state properties of two-dimensional quantum spin systems. As a spin-off we expect an efficient calculation of the energy-momentum excitations and of the thermodynamics of one-dimensional systems.

• DFG Programme: Research Grants