Topological entanglement entropy (TEE) is an efficient way to detect topological order in the ground state of gapped Hamiltonians. The seminal work of Kitaev and Preskill [“Topological entanglement entropy,” Phys. Rev. Lett. 96, 110404 (2006)], and simultaneously by Levin and Wen [“Detecting topological order in a ground state wave function,” Phys. Rev. Lett. 96, 110405 (2006)] proposed separate definitions of TEE based on a subtraction scheme. In the present work, we explain why the subtraction schemes work for the computation of TEE and generalize them for an arbitrary number of subregions by explicitly noting the necessary conditions for an information quantity to capture TEE. Our analysis puts the two definitions [Kitaev and Preskill, “Topological entanglement entropy,” Phys. Rev. Lett. 96, 110404 (2006), Levin and Wen, “Detecting topological order in a ground state wave function,” Phys. Rev. Lett. 96, 110405 (2006)] into separate classes. Focusing on cyclic information quantities ${\mathcal{Q}}_{2n+1}$ and multi-information ${\mathcal{I}}_n$, we propose a generalized framework for defining TEE. We also show that the holographic entropy inequalities are satisfied by the quantum entanglement entropy of the nondegenerate ground state of a topologically ordered two-dimensional medium with a mass gap.

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• Entanglement entropy
• Topological order
• Topological phases of matter
• String theory techniques in condensed matter