Physical proof of the topological entanglement entropy inequality

Michael Levin

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arXiv · 2408.04592

Physical proof of the topological entanglement entropy inequality

Michael Levin

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Abstract

Recently it was shown that the topological entanglement entropy (TEE) of a two-dimensional gapped ground state obeys the universal inequality $\gamma \geq \log \mathcal{D}$, where $\gamma$ is the TEE and $\mathcal{D}$ is the total quantum dimension of all anyon excitations, $\mathcal{D} = \sqrt{\sum_a d_a^2}$. Here we present an alternative, more direct proof of this inequality. Our proof uses only the strong subadditivity property of the von Neumann entropy together with a few physical assumptions about the ground state density operator. Our derivation naturally generalizes to a variety of systems, including spatially inhomogeneous systems with defects and boundaries, higher dimensional systems, and mixed states.

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Michael Levin. 2024-08-08. Physical proof of the topological entanglement entropy inequality. https://arxiv.org/abs/2408.04592

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