Entanglement spectrum and magic in higher-dimensional free fermionic systems
Abstract
We study fermionic non-local magic in higher-dimensional free-fermion systems through the lens of the entanglement spectrum. For translationally invariant Gaussian states in strip geometries, dimensional reduction maps the problem to independent lower-dimensional momentum sectors, leading in two dimensions to a multiplicative logarithmic violation of the boundary law analogous to Gioev-Klich-Widom scaling. We further show that the second Rényi fermionic non-local magic is bounded by the capacity of entanglement and introduce an entanglement-temperature deformation that probes the low-energy structure of the entanglement Hamiltonian. Applied to the matter-Majorana sector of the Kitaev model, this response is exponentially suppressed in the Abelian phase and algebraic in the non-Abelian phase, where its ratio with the capacity approaches a universal constant. Out of equilibrium, we extend the quasi-particle description to fermionic non-local magic in higher-dimensional quenches and show that random Gaussian circuits exhibit diffusive spreading in two spatial dimensions.
Related
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BibTeX
@misc{magni2026entanglement,
title = {{Entanglement spectrum and magic in higher-dimensional free fermionic systems}},
author = {Beatrice Magni and Daniele Iannotti and Riccardo Travaglino},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36008},
eprint = {2609.36008},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36008},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Entanglement spectrum and magic in higher-dimensional free fermionic systems
AU - Beatrice Magni
AU - Daniele Iannotti
AU - Riccardo Travaglino
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36008
UR - https://arxiv.org/abs/2609.36008
AB - We study fermionic non-local magic in higher-dimensional free-fermion systems through the lens of the entanglement spectrum. For translationally invariant Gaussian states in strip geometries, dimensional reduction maps the problem to independent lower-dimensional momentum sectors, leading in two dimensions to a multiplicative logarithmic violation of the boundary law analogous to Gioev-Klich-Widom scaling. We further show that the second Rényi fermionic non-local magic is bounded by the capacity of entanglement and introduce an entanglement-temperature deformation that probes the low-energy structure of the entanglement Hamiltonian. Applied to the matter-Majorana sector of the Kitaev model, this response is exponentially suppressed in the Abelian phase and algebraic in the non-Abelian phase, where its ratio with the capacity approaches a universal constant. Out of equilibrium, we extend the quasi-particle description to fermionic non-local magic in higher-dimensional quenches and show that random Gaussian circuits exhibit diffusive spreading in two spatial dimensions.
ER -