Toy model of boundary states with spurious topological entanglement entropy

Abstract

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.

arXiv comment5+7 pages, 4 figures v2:published in PRResearch: Rapid Communication. Title is modified. Minor errors are fixed

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• Universal lower bound on topological entanglement entropy
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• Quantum entanglement and non-Hermiticity in free-fermion systems
• Mixed-State Entanglement Measures in Topological Order
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Universal Spreading of Conditional Mutual Information in Noisy Random Circuits
• Anyon Quantum Dimensions from an Arbitrary Ground State Wave Function
• Many-body systems with spurious modular commutators
• Bicolor loop models and their long range entanglement
• Boundary topological entanglement entropy in two and three dimensions
• Topological entanglement entropy meets holographic entropy inequalities
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• Holographic duality between bulk topological order and boundary mixed-state order