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arXiv · 2104.11581

Entanglement of Free Fermions on Johnson Graphs

Pierre-Antoine Bernard·Nicolas Crampe·Luc Vinet
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Abstract

Free fermions on Johnson graphs $J(n,k)$ are considered and the entanglement entropy of sets of neighborhoods is computed. For a subsystem composed of a single neighborhood, an analytical expression is provided by the decomposition in irreducible submodules of the Terwilliger algebra of $J(n,k)$ embedded in two copies of $\mathfrak{su}(2)$. For a subsytem composed of multiple neighborhoods, the construction of a block-tridiagonal operator which commutes with the entanglement Hamiltonian is presented, its usefulness in computing the entropy is stressed and the area law pre-factor is discussed.

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Pierre-Antoine Bernard, Nicolas Crampe, Luc Vinet. 2021-04-23. Entanglement of Free Fermions on Johnson Graphs. https://doi.org/10.1063/5.0099879

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