A Bosonic Model of Quantum Holography

• URL: http://arxiv.org/abs/2311.01516v1
• Date: Thu, 2 Nov 2023 18:04:10 GMT
• Title: A Bosonic Model of Quantum Holography
• Authors: Brian Swingle, Michael Winer
• Abstract summary: We analyze a model of qubits which we argue has an emergent quantum gravitational description similar to the fermionic Sachdev-Ye-Kitaev (SYK) model. The model is known as the quantum $q$-spin model because it features $q$-local interactions between qubits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We analyze a model of qubits which we argue has an emergent quantum gravitational description similar to the fermionic Sachdev-Ye-Kitaev (SYK) model. The model we consider is known as the quantum $q$-spin model because it features $q$-local interactions between qubits. It was previously studied as a model of a quantum spin glass, and while we find that the model is glassy for $q=2$, $q=3$, and likely $q=4$, we also find evidence for previously unexpected SYK-like behavior for the quenched free energy down to the lowest temperatures for $q \geq 5$. This SYK-like physics includes power-law correlation functions and an extensive low temperature entropy, so we refer to the model as Spin SYK. The model is generic in that it includes all possible $q$-body couplings, lacks most symmetries, and has no spatial structure, so our results can be construed as establishing a certain ubiquity of quantum holography in systems dominated by many-body interactions. Furthermore, we discuss a generalized family of models which includes Spin SYK and which provably exhibit SYK-like physics in the solvable limit of large local Hilbert space dimension. We also comment on implications of a bosonic system with SYK-like properties for the study of holography, Hamiltonian complexity, and related topics.

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