Related papers: Quantum scrambling of algebras of observables: the $\mathbb{Z}

Quantum scrambling of algebras of observables: the $\mathbb{Z}_2$-symmetric case

URL: http://arxiv.org/abs/2606.29137v1
Date: Sun, 28 Jun 2026 00:55:02 GMT
Title: Quantum scrambling of algebras of observables: the $\mathbb{Z}_2$-symmetric case
Abstract summary: unitary quantum scrambling for an entire class of observable algebras $mathcal A'=mathbbCmathbbZ$<n>We derive exact expressions for the A-OTOC and the Plcker fidelity in the general case, as well as their values for a random unitary.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We consider unitary quantum scrambling for an entire class of observable algebras $\mathcal A$ whose commutant ${\mathcal A}'=\mathbb{C}\mathbb{Z}_2$ is generated by a Hermitian involution $S$, i.e., a parity operator. We adopt two different, although related, scrambling measures: (a) the algebraic out-of-time-order correlator (A-OTOC) introduced in [Andreadakis, Anand, and Zanardi, Phys. Rev. A 107, 042217 (2023)], and (b) a Slater-determinant-type quantity, dubbed the Plücker fidelity, obtained by embedding operator algebras into a higher-dimensional projective operator space. Both measures admit a simple geometric interpretation in terms of distances between algebras and their dynamical images. Moreover, they can be expressed in terms of the norm of the $\mathbb{Z}_2$-symmetry-breaking component of the unitary, which is in turn controlled by the time autocorrelation function of the $\mathbb{Z}_2$ generator $S$. We derive exact expressions for the A-OTOC and the Plücker fidelity in the general case, as well as their values for a random unitary. For Hamiltonian-generated channels, we compute their long-time averages, as well as the typical values of these long-time averages for random generators $S$. Finally, we numerically explore the results of our formalism for interacting spin chains in different phases and for different physical parity operators.

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