Entanglement of inhomogeneous free fermions on hyperplane lattices
| Autor: | Bernard, Pierre-Antoine, Crampé, Nicolas, Nepomechie, Rafael I., Parez, Gilles, d'Andecy, Loïc Poulain, Vinet, Luc |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Nuclear Physics B 984 (2022) 115975 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.nuclphysb.2022.115975 |
| Popis: | 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. Comment: 27 pages, v3: corrected sign typo in Eq. (4.2) |
| Databáze: | arXiv |
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