Entanglement of Free Fermions on Johnson Graphs

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.

arXiv comment24 pages

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Cited by in corpus (8)

• Bivariate $P$-polynomial association schemes
• The Clebsch--Gordan coefficients of $U({\mathfrak{sl}}_2)$ and the Terwilliger algebras of Johnson graphs
• Fermionic logarithmic negativity in the Krawtchouk chain
• Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes
• An imperceptible connection between the Clebsch--Gordan coefficients of $U_q({\mathfrak{sl}}_2)$ and the Terwilliger algebras of Grassmann graphs
• The Clebsch-Gordan Rule for $U({\mathfrak{sl}}_2)$, the Krawtchouk Algebras and the Hamming Graphs
• Entanglement of free-fermion systems, signal processing and algebraic combinatorics
• The Terwilliger algebra of symplectic dual polar graphs, the subspace lattices and $U_q(s{l}_2)$