Entropic Topological Invariants in Three Dimensions

Abstract

We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological properties is richer than the two-dimensional case. In addition to the reduction of the entropy caused by non-zero vacuum expectation value of contractible loop operators a new topological invariant appears that increases the entropy if the model consists of non-trivially braiding anyons. As a result the three-dimensional topological entanglement entropy provides only partial information about the two entropic topological invariants.

4+3 pages, 1 figure

References in corpus (3)

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• Bipartite entanglement and entropic boundary law in lattice spin systems
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• Boundary topological entanglement entropy in two and three dimensions
• Machine Learning Entanglement Freedom Or: How I Learned to Stop Worrying and Love Linear Regression
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