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Entanglement in Fermionic Chains and Bispectrality

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arxiv 2001.10576 v2 pith:NDV4OA2S submitted 2020-01-28 math-ph cond-mat.stat-mechmath.MP

Nicolas Crampé , Rafael I. Nepomechie , Luc Vinet This is my paper · ORCID
classification math-phcond-mat.stat-mechmath.MP
keywords entanglementmathfrakchainsfermionicalgebraalgebraicalgebrasanalysis
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abstract

Entanglement in finite and semi-infinite free Fermionic chains is studied. A parallel is drawn with the analysis of time and band limiting in signal processing. It is shown that a tridiagonal matrix commuting with the entanglement Hamiltonian can be found using the algebraic Heun operator construct in instances when there is an underlying bispectral problem. Cases corresponding to the Lie algebras $\mathfrak{su}(2)$ and $\mathfrak{su}(1,1)$ as well as to the q-deformed algebra $\mathfrak{so}_q(3)$ at $q$ a root of unity are presented.

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  1. Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials

    cond-mat.stat-mech 2025-05 conditional novelty 6.0 of 10

    For inhomogeneous free-boson chains, the leading entanglement entropy is (a*/6) log N, where a* is the scaling exponent of the region where the local potential vanishes.

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