Gutzwiller projections of noninteracting chiral topological phases are known to give rise to fractional, topologically ordered chiral phases. Here, we carry out a similar construction using two copies of noninteracting Euler insulators to produce a class of spinful interacting Euler models. To that end, we take advantage of the recently discovered exact representation of certain Euler insulators by a projected entangled-pair state (PEPS) of bond dimension $D=2$. The Gutzwiller projection can be implemented within the tensor-network formalism, giving rise to a new PEPS of bond dimension $D=4$. We, moreover, apply very recent state-of-the-art tensor-network tools to evaluate these phases. In particular, we analyze its entanglement entropy scaling and find no topological correction to the area law, indicating that the state is not intrinsically topologically ordered. Its entanglement spectrum shows a clear cusp at momentum zero, similar to noninteracting Euler insulators, and the spectrum of the transfer operator indicates that the state is gapped, which implies nonintrinsic topological features.

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• Topological materials
• Quantum many-body systems
• Strongly correlated systems
• Tensor network methods