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Entanglement of Free Fermions on Johnson Graphs

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arxiv 2104.11581 v1 pith:IRMPIAHS submitted 2021-04-23 math-ph math.MP

Pierre-Antoine Bernard , Nicolas Crampe , Luc Vinet This is my paper · ORCID
classification math-phmath.MP
keywords entanglementcomposedentropyfermionsfreegraphsjohnsonneighborhoods
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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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  1. The Lie algebra $\mathfrak{sl}_4(\mathbb C)$ and the hypercubes

    math.CO 2025-05 conditional novelty 7.0 of 10

    The degree-N polynomials in four variables, the fixed 3-tensors of the hypercube, and the hypercube Terwilliger algebra are all isomorphic as sl4(C)-modules, with explicit maps.

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