22 August 2024 Thu 5 pm

Tensor network states (TNSs) are one of the most powerful descriptions of quantum matter. Yet, they struggle to capture topological features of free fermion systems which can be easily represented by non-interacting band theory. In particular, TNSs with short-range correlations can only possess non-trivial one-dimensional topological labels of the ten-fold classification. In this talk, I will show how TNSs can evade these restrictions when the topological phases are protected by crystalline symmetries. Specifically, I will present a very simple and experimentally relevant model of an Euler insulator whose ground state is an exact projected entangled pair state. I will elucidate that this is made possible by optimal conditions relating to the saturation of quantum geometric bounds. Finally, I will illustrate how the corresponding TNS can be generalized to the first models of interacting Euler insulators and reveal characteristic features in the entanglement spectrum that persist as interactions are turned on.

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