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arXiv · 2103.15742

Entanglement of Free Fermions on Hamming Graphs

Pierre-Antoine Bernard·Nicolas Crampe·Luc Vinet
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Abstract

Free fermions on Hamming graphs $H(d,q)$ are considered and the entanglement entropy for two types of subsystems is computed. For subsets of vertices that form Hamming subgraphs, an analytical expression is obtained. For subsets corresponding to a neighborhood, i.e. to a set of sites at a fixed distance from a reference vertex, a decomposition in irreducible submodules of the Terwilliger algebra of $H(d,q)$ also yields a closed formula for the entanglement entropy. Finally, for subsystems made out of multiple neighborhoods, it is shown how to construct a block-tridiagonal operator which commutes with the entanglement Hamiltonian. It is identified as a BC-Gaudin magnet Hamiltonian in a magnetic field and is diagonalized by the modified algebraic Bethe ansatz.

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Pierre-Antoine Bernard, Nicolas Crampe, Luc Vinet. 2021-03-29. Entanglement of Free Fermions on Hamming Graphs. https://arxiv.org/abs/2103.15742

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