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Entanglement of inhomogeneous free fermions on hyperplane lattices

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arxiv 2206.06509 v3 pith:6E3ERUYB submitted 2022-06-13 cond-mat.stat-mech hep-thmath-phmath.MPquant-ph

Pierre-Antoine Bernard , Nicolas Crampé , Rafael I. Nepomechie , Gilles Parez , Loïc Poulain d'Andecy , Luc Vinet This is my paper · ORCID
classification cond-mat.stat-mechhep-thmath-phmath.MPquant-ph
keywords entanglemententropyparametersfermionsfindfreeinhomogeneousmodel
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abstract

We introduce an inhomogeneous model of free fermions on a $(D-1)$-dimensional lattice with $D(D-1)/2$ continuous parameters that control the hopping strength between adjacent sites. We solve this model exactly, and find that the eigenfunctions are given by multidimensional generalizations of Krawtchouk polynomials. We construct a Heun operator that commutes with the chopped correlation matrix, and compute the entanglement entropy numerically for $D=2,3,4$, for a wide range of parameters. For $D=2$, we observe oscillations in the sub-leading contribution to the entanglement entropy, for which we conjecture an exact expression. For $D>2$, we find logarithmic violations of the area law for the entanglement entropy with nontrivial dependence on the parameters.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  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.

  2. Exactly solvable multicomponent spinless fermions

    hep-th 2025-02 conditional novelty 5.0 of 10

    Four exactly solvable multicomponent spinless fermion models are constructed from multivariate Krawtchouk, Meixner, and two Rahman-like polynomial families.

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