Condensed Matter Theory Forum - Dr Carolin Wille

Generic tensor networks in dimensions larger than two can not be contracted efficiently. Matchgate tensor networks, deriving their name from applications in the graph theoretic problem of perfect matchings (dimer coverings), are an exception to this rule. Hence, they provide toy models amenable to numerical studies and have been considered, e.g., in the context of holographic dualities. In this talk, I built upon the identification of matchgates with free (Gaussian) fermionic tensors to devise an effective field theory description of random matchgate tensor networks in terms of a non-linear super matrix model and compare its predictions to numerical results.