Tensor network algorithms for two-dimensional strongly correlated lattice systems
Matthias Troyer, Philippe Corboz, Ulrich Schollwöck, Reinhard M. Noack
The simulation of strongly correlated systems is among the most challenging problems in condensed matter physics. For one dimensional systems the state-of-the-art method is the density- matrix renormalization group (DMRG), however, for two-dimensional systems the computational cost scales exponentially with the width of the system. To overcome this problem tensor networks in two dimensions have been developed, which are among the most promising tools for the simulation of long-standing problems, including the two-dimensional fermionic Hub- bard model, which is believed to be the key model for high-temperature superconductivity. These methods are still at an early stage of development, but can already now compete with the best variational methods for two-dimensional systems.
The aim of this project is the improvement and better understanding of the performance of two-dimensional tensor network methods, in particular projected entangled-pair states (PEPS). This is achieved through systematic benchmark calculations using different types of optimization schemes and variants of the tensor network ansatz. Furthermore, one of the main objectives is an extensive comparison between PEPS and the DMRG for Hubbard ladders, which will improve the understanding of the performance of PEPS in a setting in which the DMRG yields accurate results. It will also clarify for which system size PEPS outperforms the DMRG, which is still an open question. Finally, the efficient PEPS method developed in this project will be used to address relevant questions related to the physics of multi-chain Hubbard and t–J ladders.