Simulation of Fermionic and Frustrated Systems with 2D Tensor Networks

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The study of fermionic and frustrated systems in two dimensions is one of the biggest challenges in condensed matter physics. Among the most promising tools to simulate these systems are 2D tensor networks, including projected entangled-pair states (PEPS) and the 2D multi-scale entanglement renormalization ansatz (MERA), which have been generalized to fermionic systems recently.
In the first part of this talk I will present a simple formalism how to include fermionic statistics into 2D tensor networks. The second part covers recent simulation results showing that infinite PEPS (iPEPS) can compete with the best known variational methods. In particular, for the t-J model and the SU(4) Heisenberg model iPEPS yields better variational energies than obtained in previous variational- and fixed-node Monte Carlo studies. Future perspectives and open problems are discussed.