Toy model of boundary states with spurious topological entanglement entropy

Understand

Topological entanglement entropy has been extensively used as an indicator of topologically ordered phases.

• We study the conditions needed for two-dimensional topologically trivial states to exhibit spurious contributions that contaminates topological entanglement entropy.
• We show that if the state at the boundary of a subregion is a stabilizer state, then it has a non-zero spurious contribution to the region if and only if, the state is in a non-trivial one-dimensional $G_1\times G_2$ symmetry-protected-topological (SPT) phase.
• However, we provide a candidate of a boundary state that has a non-zero spurious contribution but does not belong to any such SPT phase.