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 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.
@article{arxiv.2104.11581,
title = {Entanglement of Free Fermions on Johnson Graphs},
author = {Pierre-Antoine Bernard and Nicolas Crampe and Luc Vinet},
journal= {arXiv preprint arXiv:2104.11581},
year = {2023}
}