Gapped spinful phases obtained via Gutzwiller projections of Euler states

TL;DR

This paper constructs and analyzes spinful interacting Euler models via Gutzwiller projections of Euler insulators, revealing phases with local order but no intrinsic topological order.

Contribution

It introduces a tensor network approach to generate and study new spinful Euler phases, combining PEPS representations with Gutzwiller projections.

Findings

No topological correction to the entanglement entropy area law.

Entanglement spectrum shows a cusp at zero momentum.

Presence of Bragg peaks indicating local order.

Abstract

Gutzwiller projections of non-interacting 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 non-interacting 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 non-interacting Euler insulators, and the spectrum of the transfer operator indicates that the state is gapped, which could imply non-intrinsic topological features. Finally, the static structure factor displays Bragg peaks, indicating the simultaneous presence of local order.