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Magic and Wormholes in the Sachdev-Ye-Kitaev Model

Valérie Bettaque

Published Jan 1, 2026• 0 citations
Publisher

Abstract

This dissertation is a collection of three papers written by the author and her advisor, which concern the quantum information (and more specifically quantum resource theory) properties of the Sachdev-Ye-Kitaev (SYK) model and other (fermionic) many-body systems.
DOI
10.48617/etd.1597

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Any quantum state is fully specified by the expectation values of a complete set of Hermitian operators. For a system of Majorana fermions, such as the Sachdev-Ye-Kitaev (SYK) model, this set of observables can be taken to be all possible strings of Majorana fermion operators. The expectation values of these fermion strings in a thermal state depend erratically on the microscopic couplings that specify the SYK Hamiltonian, and we study their statistical properties directly in the thermodynamic limit using path integral techniques. When the underlying SYK Hamiltonian is chaotic, we find that these expectation values are well-modeled as real Gaussian random variables with zero mean and a variance that we compute. In contrast, for the integrable variant of SYK, we find that the expectation values are actually non-Gaussian. We then use these results to study measures of magic in the SYK thermal state, including the robustness of magic and the stabilizer Rényi entropy. We also show that our results can be quantitatively reproduced with a dual gravity calculation in the chaotic case at sufficiently low temperature. In this dual gravity model the variance of a given microscopic operator string is related to a wormhole geometry stabilized by a massive particle which is dual to the operator string. Our results thus provide a concrete and quantitative setting in which to study the relationship between randomness, wormholes and closed universes, as well as a holographic dual of quantum magic.
FINDING: Traversable wormhole construction in the lab via holographic quantum simulation (SYK model) and multi-mouth wormhole topology with free group structure. | MATH: The key mathematical objects are: (1) the Sachdev-Ye-Kitaev (SYK) model — a 0+1D quantum mechanical model with N Majorana fermions and random all-to-all 4-body interactions, Hamiltonian \( H = \sum_{i 0 \) (negative energy injection); (3) for multi-mouth wormholes: fundamental group π1=F2 \pi_1 = F_2 π1​=F2​ (free group on two generators) for the three-mouth case, with the topology described by a genus-2 handlebody; (4) the ER=EPR correspondence maps entangl Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com