Pushing the frontier of simulations of two-dimensional multi-orbital fermionic lattice and Heisenberg models by fully exploiting non-abelian symmetries in tensor network states

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The interplay of spin and orbital quantum degrees of freedom in fermionic lattice models leads to highly complex competing correlated phases at low energies. For their understanding well-controlled non-perturbative methods are quintessential. A very promising new approach in that respect is provided by tensor network states (TNS) which nevertheless are extremely demanding numerically. Therefore the main focus of this project is on symmetric multi-orbital models where we aim to fully exploit all underlying abelian as well as non-abelian symmetries in order to advance TNS simulations of two dimensional (2D) lattice models far beyond the current state-of-the-art. To this end, we will utilize the recently developed QSpace tensor library that can deal with non-abelian symmetries on a generic footing. For 1D systems, this has already yielded many orders of magnitude in gain of computational efficiency. Here we will use QSpace to study the low-energy phase diagram as well as entanglement and topological properties of several paradigmatic model systems in 2D. These include N-orbital fermionic systems such as the Hubbard and tJ-model with relevance to high-Tc superconductivity, as well as derived SU(N) Heisenberg models with spin and orbital degrees of freedom that exhibit unconventional magnetism. A better computational control of these systems ultimately promises a fundamental impact on our understanding of strongly-correlated quantum many-body systems.