Entanglement of free fermions on Johnson graphs

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 subsystem composed of multiple neighborhoods, the construction of a block-tridiagonal operator that commutes with the entanglement Hamiltonian is presented, its usefulness in computing the entropy is stressed, and the area law pre-factor is discussed.

Automated summary

This paper studies free fermions on Johnson graphs J(n, k) and calculates the entanglement entropy of sets of neighborhoods. For a subsystem composed of a single neighborhood, an analytical expression is provided through the decomposition in irreducible submodules of the Terwilliger algebra of J(n, k) embedded in two copies of su(2). For a subsystem composed of multiple neighborhoods, the construction of a block-tridiagonal operator that commutes with the entanglement Hamiltonian is presented, highlighting its usefulness in computing the entropy, and discussing the area law pre-factor.