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.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2609.36008 [quant-ph]

(or arXiv:2609.36008v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.36008 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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