In strongly correlated quantum systems - except for a few special cases - the wave function and the correlations functions cannot be determined analytically.
Therefore, the proper treatment of such systems requires the development and application of accurate numerical methods.
A subclass of these numerical algorithms, that scale polynomially with system size, are in the focus of state-of-the-art condensed matter physics.
Currently the most promising algorithms used for the simulation of quantum systems are based on tensor product factorization.
Our research group have been active in this filed for more than two decades, while also exploring connections between these methods and quantum information theory.
The candidate can join this research program and work on further extensions of the density matrix renormalization group (DMRG) method, the matrix product state (MPS) and tensor network state (TNS) algorithms.
In the past years we have proposed novel approaches for long time simulation for quantum system by combining MPS and orbital basis optimization protocols.
The task of the PhD candidate is to implement and refine existing algorithms and apply them to high dimensional optimization tasks, for example two-dimensional interacting quantum many body systems or strongly correlated molecular clusters.
The proposed research program is part of several intense international collaborations.